People often act like it's a rare feat to successfully write a protagonist of the opposite sex. And this makes sense, of course, since examples of such characters only include obscure outliers such as Dorothy Gale, Victor Frankenstein, Harry Potter, Alice (of Wonderland fame), the Little Mermaid, the Little Match Girl, Marie Stahlbaum, Lyra Belacqua, Buffy the Vampire Slayer, Ellen Ripley, Wonder Woman, the girl with the dragon tattoo, Hercule Poirot, Elphaba, Peter Rabbit, Atticus Finch...
I'll just say it: Our belief that writers can't create cross-gender protagonists is crap. In fact, I'd go so far as to say that men have a better record of writing females, and vice versa. Just look at the above list; the characters I've compiled there include maybe four of the five biggest names in our literary cannon.
Why might this be? My own theory is that the opposite sex is different enough for you to step out of yourself a bit, yet the difference is still too superficial to prevent your own personality from coming through. As an example, let me present a protagonist of my own creation:
This is Destiny Curry from a novel of mine. She's female, she's small for her age, and her features are far too girlish for her own liking. In short, she's a whole lot of what I'm not.
She's also very fun to write. When she feels strongly about something, she shouts about it. When she's at odds with somebody she doesn't like, she openly insults them. She screws with people who aren't as smart as her, she tells outlandish lies just to get a reaction, and she's a very vocal proponent of her own greatness.
And she gets away with most of it, because she's a cute sixteen-year-old girl. She's so physically unthreatening that her worst boasting, goading, and shouting seldom has the power to do anything worse than annoy. In fact, one of her own biggest lamentations is how her proportions make it difficult for people to take her seriously as a potential menace.
When there are things I have trouble expressing, it's because I need to put a lot of effort into not frightening people. When there are things that Destiny has trouble expressing, it's for the opposite reason. This is why it's so liberating to write in her voice, and why I imagine that, if she were to write a novel, her protagonist would be a lot more like me.
By contrast, characters written by authors of the same sex often seem to be problematic. Obviously there are many well-written or successful examples, some of which are notably well-written and successful at the same time, but it's clear that there are obstacles to overcome. Consider as examples Bella Swan of Twilight fame and Eragon of Eragon; both were written by an author of the same sex, both can easily be accused of being author-insert protagonists, and both can be reasonably described as unintentionally shitty people. The former is such an over-romanticized "beautiful swan" that the world inexplicably tears itself apart out of fascination for her feckless, moony attentions. The latter is a whiny little Star Wars wannabe who exhibits a thunderous sense of entitlement to command the lives of kings and nations based on the fact that he can kill people with his dragon.
In short, both of them take their respective genders and crank them up to the worst, most poisonous stereotypes associated therewith. Their authors, like myself, are pushing against the social constraints they feel in their own lives, but instead of putting themselves into the shoes of someone who wasn't bound by the same rules, they elected to write versions of themselves who don't have to be bound by any rules at all. And it's hard to write a character like that without writing a piece of shit.