The hatred is mostly from it forcing specific strategies for simple tasks. The intent is to help students gain better intuition for math and gain multiple problem solving tools. But you end up with children who didn't understand the lesson taking homework to their parents who know a "simpler" way not understanding what's being asked for and everyone getting frustrated. I fully understand, in school my issue was always getting marked down for not being able to show my work for mental math.
A lot of the bad examples of it you'll see are just poor teaching (e.g. the "3 x 5 can't be 5 + 5 + 5, it's 3 + 3 + 3 + 3 + 3" image), and we had that before Common Core. That guy's "batshit insane" example is just a slightly obtuse word problem.