Why to breed the growlithe? Because the only growlithe available in-game as of now is the one of that event. If you trade it away, you cannot get anymore growlithes the legal way. If you breed it you'll have two, so you can keep one and use the other for the azurill trade.
Keeping growlithe is your call. I don't care about it so I traded it, but other people might wanna know there will be no more growlithes before trading it away XD