men can identify and empathize with male as well as female protagonists, while women identify better with female protagonists (the claim being, they can certainly sympathize with male protagonists, but identification is harder).
Anecdotally, I would consider the reactions of a percentage of male fans to the all-female Ghostbusters, Daisy Ripley's Rey in The Force Awakens, and the female lead of Rogue One, just in the past year, to refute this assertion.
Obviously I am also speaking in gross generalities, but seriously: male leads have dominated fiction in most media for, like, millennia. American fiction is finally reaching a point where female leads are starting to show up more often in bigger-impact works, and a certain subsection of the audience is losing their tiny bigoted minds. These men don't want women to be protagonists in the entertainment they interact with because they cannot empathize or identify with female protagonists. Those female-led stories are outside their experiences, and it makes them uncomfortable and upset when they, and their stories, are not the focus of the tale being told.
There have primarily been male protagonists for a significant majority of time and fiction, so by default, any female readers would only have had male protagonists to emphathize and identify with. Women simply haven't had the option of a woman being the main character driving the story in a Star Wars movie before now. Not that Leia didn't kick ass and keep her head, but the journey was clearly Luke's. So little girls had the option of playing "Leia, the sidekick and love interest," or pretending to be the hero, Luke who is male. (Or Han, the snarky sidekick. I confess I never met anyone who wanted to be Chewie.) Now little girls can be Rey.
I have no particular statistics to back up my assertions either. I think the answer to your question may be yes, but in the opposite way your friend claimed.