I was thinking the same, it's not aiming at any gender as far as I can tell. I took it as a wink at the "men always want sex, no exceptions" stereotype/gender norm. But, I'm a man and all that proves is that the slogan is vague enough that each reader will have their own personal interpretation of it's exact meaning based on their own experience.
In that sense it is indeed a terrible slogan if only for the fact that it seems to elicit a negative, but highly personalised, meaning for everyone. The exact opposite of what you hope to achieve with a slogan.
No, it doesn't. It shows mild anger at being insulted for no reason. Are you running on the assumption that he's asking her out in this scenario? The only rejection he got was unsolicited. Like if I walk up to the next woman in the street, ask if she's single and when she says "yes" I respond "nevermind, you're not good enough". Now she's upset and understandably so.
I'm in full agreement with your point, but this comic is not a representation of that in any way.