Sure it comes with it's share of problems, the most obvious is guitar. Not every shop carries lefties and they may come at a higher price... well they use to, not sure now.
I don't beleive in forcing someone in playing righty. You're righty or you're not. If it feels more comfortable playing lefty than by all means, play lefty.
I've never came across a logical reason why everyone should play righty. Ever.
I would love to hear why your teacher suggested that. My guess is that he's going to say because most of the gear are for lefty. For me, that is not a reasonable answer.