I begged my mom for boxers (briefs are icky to me XD), but she kept saying no because she knew it wasn't just to sleep in, and she felt it'd be "crossing a line". She ended up letting me get crappy cotton ones to swim in, then later when they were all I wore, gave in and let me buy a pack of men's boxers.
If you have the money, I suggest just buying your own. It's none of your dad's business, really. Say they're more comfortable. Or if you're into that expensive "slowly does it" stuff, you could go for boyshorts or sports undies, or maybe patterned boxer briefs? XD My chick friend has one pair of boxer briefs identical to mine.