What specifically is wrong with Common Core math? I've seen a lot of vague complaints about it but the materials my children brought home seem fine. It's different from the way I learned but I haven't seen any compelling evidence that it's worse.

Yep. From what I recall from my time in education about a decade ago, Common Core standards were generally considered excellent. The rollout of Common Core tests wasn't that great, but that should have been a one-time adaptation period, but everything got mired in politics and bit by bit got torn apart as states all went their own way.