The idea doesn't bother me, but specific instances of execution certainly could. I've been lucky in having mostly very good players, so I've never run into a real problem with it. And the few problem players I've had haven't had that as one of their problems. 
Bottom line: It's your game. It's not my game, so my opinion of it doesn't matter that much. If it's going to wig you out, then whether or not it's silly, it's not good for the game. If you think that the players can't do it in a mature and reasonable fashion, or if you are just icked out by the idea, then say as much and close the door on the discussion.
If you want to give it a try, give it a try in a short game -- a 3 or 4 night mini-game that will let people play with new characters (and letting the dude run a female PC). If after 4 sessions, it still irks you, then just say so. You're not DMing to expand your boundaries and challenge yourself. You're DMing to have fun and help other folks have fun. If, though, it seems okay after 4 sessions, maybe you could let him bring the PC in -- with the understanding that you'll write "her" out of the story in a hot second if you become uncomfortable.
If I was a new player in a game with a DM who felt that way, and I really wanted to play a female PC, that'd be acceptible as a reasonable compromise. And if I was a new player and a DM had a strict "No Cross-Gender" rule (ie, Teflon Billy, who's been burned often enough that he doesn't want to get burned no more), I'd shrug and be fine with it. I've got a lot of character concepts I'd like to play -- for me, it's fun exploration of a character, not a chance to work out deep emotional issues.
Bottom line: It's your game. It's not my game, so my opinion of it doesn't matter that much. If it's going to wig you out, then whether or not it's silly, it's not good for the game. If you think that the players can't do it in a mature and reasonable fashion, or if you are just icked out by the idea, then say as much and close the door on the discussion.
If you want to give it a try, give it a try in a short game -- a 3 or 4 night mini-game that will let people play with new characters (and letting the dude run a female PC). If after 4 sessions, it still irks you, then just say so. You're not DMing to expand your boundaries and challenge yourself. You're DMing to have fun and help other folks have fun. If, though, it seems okay after 4 sessions, maybe you could let him bring the PC in -- with the understanding that you'll write "her" out of the story in a hot second if you become uncomfortable.
If I was a new player in a game with a DM who felt that way, and I really wanted to play a female PC, that'd be acceptible as a reasonable compromise. And if I was a new player and a DM had a strict "No Cross-Gender" rule (ie, Teflon Billy, who's been burned often enough that he doesn't want to get burned no more), I'd shrug and be fine with it. I've got a lot of character concepts I'd like to play -- for me, it's fun exploration of a character, not a chance to work out deep emotional issues.