Last night, when the flight was cancelled, there were severe storms affecting JFK, so it could still be a possible weather issue. I think you can look on Expert Flyer to see the reason, if you've got access to that. Edited to add: it looks like last night's AA flight from SFO to JFK cancelled, so the plane didn't make it in for the 11am flight today. A JetBlue flight yesterday from SFO-JFK had to divert to ACY, but that was earlier in the day, so still can't say if the AA cancellation was due to weather.

Was there no availability on the other AA flights today either?

Not saying you did anything wrong, but for the future, if you booked through JetBlue, even though the flight was on AA, I would've tried calling JetBlue while waiting for the callback from AA to see if JetBlue could've helped you. They might've been able to get you on the JetBlue flights.

With the cancellation, if you want the refund, instead of taking the flight, you should be able to get that. They won't give you a refund if you still take the rebooked flight though.