I agree that men are expected to be assertive, but socially apt? Not unless they have some sort of title or high position, otherwise it's pretty common to joke about how horrible men are in social situations. Women are the ones expected to be socially competent as far as I've seen/heard.
I can't give examples on how people have treated me in real life on a personal level since I haven't allowed one. I think that society generally views reserved and friendless people negatively no matter what gender, the view of them is just a different type of negative. (lonely men=creepy and untrustworthy, lonely women=insane cat lady, desperate to be with anybody)
I also think the idea expressed in that picture is a bit unrealistic and dismissive towards females with anxiety issues, as if it's not a big deal because there are tons of (imaginary) people waiting to help you out because you're just so kawaii.

When I used to talk to people on the internet (mostly males) almost all of them thought my severe social anxiety was weird, not sweet and endearing like the picture suggests.
Short version: They're both ****ed.