Read other letters about this article
which is the one element of all this that the author misses.
Since it's the only element that really matters, that's a fairly large one to get wrong.
Thinking that you can logically persuade people to use one term versus another because of etymology is a tried and failed strategy. Language follows rules but not the ones that people like the author of this imagine that they do. They're laws of dissemination, usage, trenda, and so on. Steven Pinker makes good reading for more on how it works.
Words mean what we decide they mean. For lots of complicated reasons, some of which the author describes here, the terms have changed. Progessive is what people call themselves more often now, and it's going to stick. You can call yourself "a liberal" if you want, but it mostly the right wingers who use that term now, and in entirely negative ways. Since the right wingers are quickly losing all the influence they had, that word will soon go with them.
Sorry, that one is done.