Yep. His Mom. In this nice interview with Dan Roche (whom Josh must like--he has no compunction about limiting his interviews during Spring Training), Josh mentions how his Mom gets angry at him when he 'acts out':
Beckett: I dunno, I think emotions are not premeditated for me, you know, generally whenever I do the things that my Mom hates whenever I do, it's an emotional deal. It's not that you don't know what's going on but it's just like, it just pops out...it's a spur of the moment deal.
Beckett's as laid back and cool during this Q&A as you could possibly expect anyone to be, which further confirms my dad's analysis that it's not so much that he likes to drop f-bombs all the time as that he has a tendency not to be able to snap out of 'angry pitching mode' before his post-game pressers.
However, this interview also confirms my corollary to that theory, which is that he doesn't appear to be able to speak for very long without swearing just as a matter of habit--behold the half-mumbled "and shit like that" when he's describing aspects of his off-season workout routine. Even as he's saying it he seems to catch himself--hence the mumble--but there it is, anyway.
Which kind of sums him up in general, if you think about it.