What are disasters with Axiom of Determinacy?

It might not be a disaster, but I've always thought it counterintuitive that there is an equivalence relation on the real line with strictly more than continuum many equivalence classes. The equivalence relation isn't even very complicated; it's just congruence modulo $\mathbb Q$ in the additive group of $\mathbb R$. In other words: Vitali wants to give you his standard example of a non-measurable set, and, if you prevent him from doing so, he gets his revenge with this example of partitioning a set into strictly more pieces than it has elements.

Determinacy arguably leads to some disasters in cardinal arithmetic. For instance, under AD we have that $\omega_n$ is singular - that is, can be written as a union of fewer-than-$\omega_n$-many sets each of size $<\omega_n$ - for all finite $n>2$. See Asaf's answer to my question on arithmetic in AD.