Wikipedia disagrees as does every other definition I found.

Centrism is a political outlook or position involving acceptance or support of a balance of social equality and a degree of social hierarchy while opposing political changes that would result in a significant shift of society strongly to the left or the right.

The far left and far right each have some funny ideas that aren't fair to the rest of the country in America (and in some cases the world). Thinking about how best to move forward while getting as many people on board as possible and affect real change doesn't mean "Hey other side, get fucked. Civil war time because I can't have everything I want in all scenarios!"

The "false dichotomies" that you're speaking about are simplifications to get the point across and are not false. You can feel that there needs to be a better system and that people in power shouldn't be able to ignore issues that they find uncomfortable so that riots are not needed, and also be opposed to destroying things belonging to people not in power. There is nothing false about that.