It always amuses me when anyone says that men write and read he-manly ass-kicking action stories because they aren't good at empathy or relationships. The vast majority of the great male writers of the 18th and 19th centuries would like to have a word with you.
If I had to compare one "classic" to Twilight, it would be Jean-Jacques Rousseau's endless obsessive romance La Nouvelle Héloise, which was immensely popular with both men and women in the 1700s but is almost unreadable, I would wager, by anyone of either gender today. Likewise, Pamela, the blockbuster novel of the 1740s? Female MC, male author, utter wish-fulfillment that seemed to work for readers of both sexes, creepy woman-in-peril rape fantasies and all.
At some point in the late 18th century, certain female writers started outselling men, and that may be where the present-day gender divide began. Male authors felt threatened, so they declared their work more "serious" and less romancey. Even so, they often had female MCs and relationship-driven plots (Anna Karenina, anyone?), or their male MCs were introspective and angsty, not Hemingway two-fisted types (see: Crime and Punishment). Even a recent classic like The Great Gatsby is more about relationships than it is about ass kicking.
So, anyway, historical perspective makes every era look a little crazy. It sucks that guys today won't read Jane Austen because they think she's a romance writer, but that has more to do with modern marketing than with reality.
I tend to write my female MCs cold and analytical, with romantic feelings they repress, and multiple agents have told me I needed to warm/soften them up and enhance the romance angle. I've done so, because that seems to be a real necessity in the current market (and sometimes it does improve the story), but I've tried to take my warming up in a Katniss Everdeen direction and not in a Bella Swan one. It makes me sad that taking those little steps toward romance (or having a female MC at all) could eliminate a male readership, but if that's how it is, so be it.
I worry more that my book won't sell because it has a male co-protagonist, whom I tried to make a pretty plausible teenage boy.