If you can't imagine yourself as anything but a man you're obviously going to have problems with it.
Expecting that the world will always cater to your specific sex and race, providing it by default so that you can be comfortable, is what we call 'privilege.' And you get it, most of the time. Pretty weird to be denied it, huh?
Indeed. It's weird. Especially because you're trying to tell me a story.
If you're writing a book, or a movie, the audience has the option to be an observer, an unrelated third party.
However, in the medium of the game, the audience is confined to the shell of a character. Generally, you want your audience to identify with the said character in order to provide immersion. Creating a jarring difference between what you really are, and what you're told you are alienates your audience to a certain degree, because you're forcing them to play a role that they aren't, and thus they become less willing to do what you want them to do, detracting from the effectiveness of your narrative. Less of it gets through.
I can imagine myself as something that I am not. It doesn't mean that I won't be conscious of the fact that I'm imagining myself as someone else. I can feel sympathy without feeling empathy, but one is stronger than the other.
Let's take a metaphor. I can take a walk in someone else's shoes. Doesn't mean that I'll think that they're mine, doesn't mean that it'll be comfortable, doesn't mean that I'll understand how it is for
them to walk in
their own shoes from it, though. Of course I can guess at it, but forcing me to wear their shoes doesn't help me do that, it just gives me sore feet from wearing shoes that don't fit. Now, ask me to take the same walk in my own shoes and maybe I won't be distracted in looking at everything else you want me to see while taking the walk.
So, should you tell someone to wear someone else's shoes? In my opinion, not without good reason. Maybe you
want them to feel uncomfortable about it. Maybe you
want to make them feel detached and alienated.