A protest can incite insurrection. When a protest incites insurrection, it does not mean the protest was not a protest, nor that the people participating in the protest were not protesters.
If the protesters are lying about what they were protesting, just what do you think they were rallying for, and why do you think they were lying and pretending to protest against something else (and just what do you think would that accomplish, exactly? to take your "what if this happened in the US" example, if people marched on Washington demanding ... immigration reform, but what they REALLY wanted was ??? more progressive taxation, just how would that make sense, and how would their protest accomplish anything they desire?)
BTW, I never made those 3 leaps. I also never said that most Ukranians favored the protest (whether or not they favored overthrowing the government is another discussion and I have no idea if they did, but I'd venture a pretty safe guess that more people were for overthrowing the government by late February than were for the protest itself due to the government's handling of the situation)
Similarly, to take your "what if this happened in the US" example - if a protest which at its peak included nearly 6 million people (the relative proportion of the United States population) in DC on any given popular issue, PLUS multiple instances of hundreds of thousands protesting in other major cities across a significant portion of the nation, and the government responded with force resulting in hundreds of deaths and thousands of casualties, there would be a marked increase in pressure on the government beyond the original purpose of the protest (re: public opinion would certainly start to turn on the government once the government started killing citizens).
Also, since you brought it up, according to polls conducted in Ukraine in December, about half the nation (45-50% of the population) supported the Euromaidan protests while 42-50% opposed it. In other words: Euromaidan was a popular movement.