The steel-man position here — and I say this as one who does not believe in any of the many variations/presentations of the Christian god — is that "answer" does not imply "does what you ask".

What does indicate that the claim "God answers prayers" is false, is the near total lack of personal responses to those praying*, not even so much as "your prayer is important to us, you are number 184,693,224 in the queue" that I'm sure is an SMBC comic but cannot find easily on Google right now — if I had even once had such a clear and obvious statement ringing in my ears when I went through a Catholic school, I wouldn't have switched to Wicca before giving up on religion entirely.

(Not that Wicca gave me direct answers to prayers, just that it never claimed it would, either — Doreen Valiente and Janet & Stewart Farrar were both very clear about having made up the rituals themselves).

* Almost all such people, at least. Just as the number of people who claim to be able to physically shape-shift into werewolves is very small but not zero (guess how to join the dots between me knowing this and having had an interest in Wicca), the number is small enough that… other… causes are more plausible than the divine.