I'm an admin on a website and chatroom designed primarily for teens and college students-I get the 'but what about my rights?" freedom of speech thing all the time. My favorite example is to point out to them that despite freedom of speech, it is still illegal to stand up in the middle of a crowded theatre or concert hall and scream "FIRE!". It's called inciting a riot. Anybody who doesn't accept my explanation, well they get a boot off the server, and then a 5 minute ban if they come back and persist in being a jerk. I double the 5 minutes every time they come back and 'shout' back (typing in all caps, continuing to use expletives). Most of them get the idea before I get to an hour long ban, lol.
I find it more disturbing that you describe what happened as a temper tantrum than the language thing itself. Being a soon-to-be father (first time), I have concerns about how I was raised, and the possibility of continuing a cycle of violence. I've read a lot of books and articles about this sort of thing, the percentage of abused turned abuser is very high, apparently. Still, that being said...I think if my kid let loose a string like that in a tantrum, I'd be tempted to turn 'em over my knee but good. Whereas if I simply accidentally overheard them 'cuss a blue streak', I'd be more inclined to pretend I hadn't heard.