I'm not sure I agree, but I appreciate your response. I think the question is whether "left" always means progressive, and whether "right" always means conservative. For instance, I would not claim that the American right is very conservative these days, but they also don't feel "leftist" whatsoever. I don't want to really delve into political topics, however I feel strongly that what is currently going on with executive orders and gutting the executive branch workforce is not conservative whatsoever. It's more closely matches an unfamiliar kind of progressivism than it does conservatism in my mind. I could definitely understand how and why someone wouldn't agree with this, of course. I also think it could potentially be argued that leftist programs, such as entitlements, social programs, etc, are not necessarily "progressive." There could be ways these programs were strictly regressive. (and by that I mean "past-looking" rather than "bad.")
Now, I would also agree that terms like left, right, conservative, and progressive are not really strictly defined a lot of the time. With such loose definitions it might be hard to claim that I've got the definitions correct. In other words, they may just be no strict definition, and I think you could also argue that _I'm_ the one taking a minority definition.
Progressivism itself is an interesting topic in general. I think there is a lot of progressive thought which is strictly apolitical, but is definitionally progressive. An easy example would be video games. Is Doom 2 better than Doom 1 because it added more gameplay elements? Is Doom 2016 even better because it added so many more systems, and has more advanced graphics? In my opinion "apolitically progressive" gamers would almost always claim yes; things _advanced_ and having advanced the older media is inherently inferior. They would claim that the older Doom games are "janky" which is shorthand for "the older games have not adopted or anticipated modern conventions." Other folks take a different tact; they tend to dislike any newer advances in gaming, and get "stuck" preferring older games. Others take a more balanced approach; they appreciate both new and old games, but don't necessarily prefer something merely because it's newer.
I think movies are another interesting example. I think it could be argued that there are potentially objective improvements when it comes to movie making; cinematography would be one example. The movie Citizen Kane and the Director Alfred Hitchcock created totally novel approaches to cinematography which been widely and thoroughly adopted by filmmakers of all skill levels. (in other words, nearly everyone agrees that these are objective advancements) Even some of the worst movies nowadays may have more competent cinematography than some of the best movies from the 50s and 60s. On the other hand, there are clearly a lot of stylistic aspects to film-making which cannot really be said have to improved, but merely changed with the fashions of the times. I would argue that strongly-progressive-minded folks would not be able to see this; they'd see any older movie as inherently inferior, and see movies through a lens of progress. In other words, movies were always going to "advance" to where they are now, and anything older is inherently inferior. (and this is true even if they can still appreciate the movie.) Now, this is what I might call "hard apolitical progressivism," and is not necessarily the most common view out there. It's a useful example because of its explanatory nature.
It's easy to see how this mentality _could_ map to politics, but I guess my point is that it doesn't necessarily do so. And, even when it does map to politics it doesn't necessarily follow that people on the left are always progressive and people on the right are always conservative. (although I'll obviously admit that this trend is _usually_ true; the left tends to be more progressive on average, and the right tends to be more conservative on average.)