The Common Core is the one thing in modern politics that is capable of generating agreement between right-wing conspiracy nuts and left-wing conspiracy nuts: the Left hates it because they think it's an attempt to undermine teacher's union, and the Right hates it because they think the Feds are trying to undermine local control of schools. So everybody hates it.
But seriously, have you actrually read the standardds
. There's nothing especially objectionable in them, and there is a lot to like. Implementation, particularly an over-emphasis on standardized testing, could well present a problem, but the standards themselves are pretty clearly positive.