Why not? We got female Mercenaries. I suppose gender-locking classes is "traditional" for the series, but I don't really see it as necessary. I don't remember where I had seen it, but fans have made some awesome female Fighters.
I personally think IS kinda dug themselves a hole with some of the gender-locked classes. Especially towards the more ridiculous ones, I question why we have these restrictions in the first place. At the very least, creating a personal Avatar shouldn't have such restrictions on what class he/she can change into.
I do think IS is doing a good job portraying both genders in terms of having equal power and especially in Awakening, I think it's a good step forward. In particular, I really like the additions of female Mercenaries and War Cleric (axe-wielding Lissa ftw!). I really like female axe-users, and I'd love to see female Berserkers in the future. However, like I said before, I do find some restrictions silly. Males can ride horses. Males can also use Staves. So why can't we have a male Troubadour? IS did try to justify Pegasus Knight being an only female class (and I know there are people that would rather have these restrictions), however, I do really think it's faulty.
But seriously, who wouldn't want a trap Pegasus Knight? :3
Tbh, I was disappointed that Inigo couldn't become a Dancer (and I think IS missed a good opportunity to include a male Dancer). Dude has a passion for dancing and can't become a Dancer. Wut? Even if having two Dancers may break the game, there are plenty of ways to avoid problems and balance things out. In the end I don't really see any excuses.
Yeah, I'm just heartbroken that I could of potentially had a pink-haired male dancer... My dreams... crushed... Guys I may not recover form this. This... this scar may never heal!! Why would you do this to a poor gal, IS!? Whyyyy!!... Jk, jk. ;P
Sorry, I don't mean to make a huge deal about this or anything haha...