Gfrktyl

Almost every term can be appropriated to gain a positive or negative connotation.

Even the term "Fascist" used to have a positive connotation once. It was derived from the Italian word "fascio", a bundle of rods. The symbolic meaning was "strength in unity". Who wants to openly admit they are anti-unity? That was before the Nazis murdered a couple million people and conquered most of Europe in the name of Fascism. Now "Fascist" is pretty much the worst insult you can use in a political context.

Another such term is "Globalist" which once had a positive connotation but was recently malapropriated by the alt-right as a negative label to put on their opponents.

So if you associate a positive term like "Progressive" with negative effects often enough, the term itself gains a negative connotation.

It is of course also possible to do the opposite and appropriate a negative term and turn it into a neutral or even positive term. A good example is the term "gay". It once was a slur used to discriminate homosexuals. But nowadays no politician is ashamed to claim to "defend gay rights".

Now regarding the question: Why invest all the work to give a negative connotation to the self-description of your political opponents instead of using your own term which is already negative? Because it allows you to turn your opponent's reputation against them. When you convince people that "Progressive" is a negative term, then any situation where your opponents call themselves "progressive" can be used against them. The term becomes a "dog whistle". Your opponents think they are describing themselves positively by calling themselves progressive, but your followers perceive it as them admitting their malicious intentions.

In your question you cite convervatism as being a neutral term. But then I could reverse your question like so:

"conservative" is a neutral word. It tells us that you want to "conserve" something, but that something may be both good or bad or irrelevant, so the word doesn't imply anything about the moral implications of being a conservative. So why do those on the Left appropriate a neutral term and use it to denigrate their political opponents? Won't it undermine their attempted slur when people don't fall for it?

Conservatism, in the modern political discourse, is anything but neutral. "Conservative" and "Progressive" et. al. aren't just descriptors, they're membership cards: they mark someone as one of us/those people we hate. Sides have been chosen.

Words carry any semantic burden we agree that they do. But by the logic of your question a group could choose an undeserved positive label and run with it: as long as enough people accept their self-bestowed label it makes more sense from the opposition perspective to shift the semantic via the tribal mechanism than to try to kill a wide-spread meme (the label itself).

The American right is quite diverse, but there are reasons why people of various philosophical and political bents wouldn't mind labeling their opponents progressives.

Classical liberals

This group is made up of people who love the American founding and the ideas of life, liberty and property that shaped early American political thought. For many years the American left was known as liberals. To have classical liberalism associated with big government paternalism in the modern left really aggravates these people. For Example:

Here I make a plea, addressed to conservatives and libertarians,
regarding the word liberal: please do not describe leftists,
progressives, social democrats, or Democrats as “liberal.” I do not
ask that you describe yourself as “liberal.” Continue to call yourself
“conservative” or “libertarian.” I propose only a single step: don’t
call leftists “liberal.” By this single step, we can make great
strides.

Many on the right want to take back the term liberal and use it to describe the negative rights loving liberals of the 1700s. They think liberal is a misnomer when it comes to today's left. But then what should they call modern Democrats? Progressive is a term already used. Silly notions of "the right side of history" and progress are much less a concern to classical liberals than taking back the word liberal from the left.

Radical Libertarians

Radical libertarians actually do care about progress. They want to change the world into one that is free of the coercive hand of government. They, of anyone on the American right should care about this misuse of the term "progressive." Actually, not so much. The term progressive in American politics is a loaded one. It dates back to the progressive movement in the early 20th century. However only a few sentences into the Wikipedia article on the progressive era we run into the line:

Many progressives supported prohibition of alcoholic beverages,
ostensibly to destroy the political power of local bosses based in
saloons, but others out of a religious motivation.

This line taints the progressive movement's legacy irrevocably for radical libertarians. In their eyes, prohibition is a classic failure of government action; it's the worst kind of meddling in non-violent free action. Radical libertarians would love to label their opponents as progressive. The failures (in their eyes) of the progressive movement in the 1920s are exactly what radical libertarians would love people to think about when modern progressives ban straws to try to tax soda.

Philosophical Conservatives

Finally, philosophical conservatives have no problem with labeling their opponents as progressive, because they fundamentally believe that it is better to conserve than to progress. Conservatives are quick to look at the failures of utopian revolutions as the result of an obsession of progress instead of an emphasis on conserving the good with prudent reforms. Michael Oakeshott's definition puts it succinctly:

To be conservative, then, is to prefer the familiar to the unknown,to
prefer the tried to the untried, fact to mystery, the actual to the
possible, the limited to the unbounded, the near to the distant, the
sufficient to the superabundant, the convenient to the perfect,
present laughter to Utopian bliss.

A conservative doesn't hate progress, but to him, an overemphasis on progress is unhealthy and dangerous. Conservatives are happy to let their political opponents be defined by an obsession with progress. They often point to movements obsessed with progress like France in 1789 or Russia in 1918 that quickly turned to poverty and bloodshed.

This answer doesn't, however, explain why populist nationalists like Donald Trump would be okay with labeling their opponents as progressive. Anecdotaly, I have noticed that Trump seems to use the term liberal more than progressive to describe his enemies on the left.

Here's the dictionary definition for conservative:

holding to traditional attitudes and values and cautious about change or innovation, typically in relation to politics or religion.

In this case Progressive is very clearly the opposite, progressives are less cautious about change and innovation (in relation to politics and religion at least).

Perhaps you shouldn't be so hasty in calling all progress inherently "good"--the balance is important.

As someone who's a right leaning libertarian, I can answer anecdotally:

because it's a branding that is concise and understandable by most people (because "everyone" else uses it).

That's it, no more no less. I used to call them "liberals" when that label worked (proof: my earlier answers on Politics.SE). Then it stopped being accurate or widely understood by either side, so I switched to "progressives". For all I care in 5 years I'll call them "Dilwunians" if that will be the most effective method of communicating the concept at the moment.

I would use "regressive" only when my audience is such that will understand it (all 1000 of them in the continental United States who listens to Dave Rubin) - not really for propagandist purposes but more for "I'm one of you" kind of social in-group-speak purposes.

Additionally, the reason this is happening in the broader society is probably because the hegemonic power over language is, effectively, left of center - a predominant majority of journalists, entertainment figures, portals (e.g. see Google Doole politics) and less importantly college professors and teachers are politically left (yes, there are polls and surveys backing that up for people who like to call that fact of life "conspiracy theory"). As such, in full accordance with Gramsci's theories (whatever one thinks of his economic views, he was devastatingly accurate on his sociolinguistic ones), popular language usage patterns are "more friendly" towards the Left, with many many examples beyond just "progressive/liberal vs conservative".

Pardon me, no references handy, so just a drive-by.

Thomas Sowell describes the difference between conservatives and progressives as rooted in the essential vision of human nature. Progressives believe that humanity can be perfected through the efforts of enlightened leadership to forge an enlightened society. They wish to PROGRESS away from that which is bad, toward a more enlightened alternative. Conservatives believe that society should be organized to accept the limitations of humanity, which cannot be perfected, through the wisdom of those who came before, encoded in our culture and traditions, often invisible to even the most enlightened. They wish to CONSERVE that which is good, preserving it from capricious social engineering.

These map fairly neatly to large government and small government points of view, "take care of X, only government can solve it", vs "leave X be, government will only mess it up".

This is a shoddy paraphrase, but I hope that it illustrates why many conservatives embrace the label "progressive" for the left. It also helps to avoid the term "liberal" which has become muddled over time and between polities.

In the absence of a citation (other than to mention Sowell's book "A Conflict of Visions", later re-worked as "The Vision of the Anointed"), allow me to lean upon personal experience: I am a conservative and I think that labels connected to principles underlying positions, such as Progressive and Conservative, are useful for their honest descriptive power.

All change is not progress. Conservatives take change slowly and ideally in accordance with a fairly strict adherence to The Constitution. Progressives seem to not really care much about The Constitutionality of the change they want.

One example is the DACA executive order that President Obama signed into law. We have pretty well defined immigration laws (laws created by The Congress) and Obama swiped them away in an un-Constitution move. The order will likely get struck down when it hits the Supreme Court as the President doesn't have this power.

An example of doing things the right way (i.e. by the Constitution) is where President Trump looked at long standing (and failing) requirements on criminal sentencing. These sentencing problems were created by the Clinton Crime bill in 1994. After seeing that the experiment had negative consequences he has negotiated with Congress to remove some of the hard requirements on sentencing and return to allowing judges to have more leeway in making sentencing decisions.

So, the conservative idea is to think things through (I know we're talking about politicians here and thinking is not always involved) then implement and then evaluate and adjust.

Edit to provide clarity to the answer. The question, as asked, requires a deeper level of understanding of what the context of the situation is. Here you are right to assume that the words themselves are innocuous. They are, as defined, neutral or positive.

However, the words are not being used as defined. In political context, they are labels, names, or identifiers. Conservatives disagree with the "progressives" opinion of what is considered real progress. So the label means completely different things from each side of the coin talking about it.

It is, in a simplified manner, the same as a novice footballer claiming to be able to win the World Cup alone from the perspective of a conservative. Their version of "progress" is utter nonsense. So, since they self-identify as "progressive" it is used pejoratively from the "conservative" side.

You can see the the exact same thing happen with the word "fascist" when you look back at it.

It is political rhetoric. Pure and simple.

The political climate of the United States has never been friendly. From the founding of the country it has been vicious.

"The alternate domination of one faction over another, sharpened by the spirit of revenge, natural to party dissension, which in different ages and countries has perpetrated the most horrid enormities, is itself a frightful despotism." - George Washington 1796 farewell address

Quote from here.

Basically, you're asking a question that was warned against doing since we started doing it hundreds of years ago. It is not unique to any side.