Parents are often right, but then again, one of my friends (who is turning 20 this year) has parents who won't even let him leave the house without knowing exactly where he's going and for how long. Parents are sometimes right, but not always.
In regards to TF2... I think the best way to get them to understand is do your research; one of the posters here has already given you an article; but there are far more. Gather a bunch of articles which prove your point for you (and which aren't being argued by 12 year olds, articles like this are usually written by professors studying the effects of violent gaming). Go for the ones which show that gaming is actually an educational process which even the violence can be over-turned by the fact that the good outweighs the slight bad. For example; TF2 actually has it's very own economy - which funnily enough taught MY 10year old brother more about economy than anything else.
As it stands though; it may be they will continue to say no to prove a point more-so than because they believe in their answer. In which case, you're just going to have to wait a couple of years.
But I disagree with other posters here; I remember when I was 14/15 and my step father banned me from the internet at home (the ban was going to last until I left home). It took me 4hours of arguing, but luckily for me, my step dad knows when he is beaten and I won my rights back to the internet. The best arguments are more debates in nature. You need to be prepared to fight your case - not get frustrated, but continue to push your point in a logical and concise way.
Good luck mate.