Marriage. He's terrified of it.
His father told him time and time again the only person who has ever truly seen under his mask is his wife, Ebisu's mother. Only she knows all of his insecurities and weaknesses, his flaws and his nightmares. And she has been sworn to secrecy as a good, loyal wife, who would never leave him or judge him.
Dear god, Ebisu thinks every time he looks in the mirror. How am I supposed to find someone like that? I can't even find someone who doesn't detest me.
The closest thing he has to friend is Iruka, and Iruka is a man.
And as for attracting a civilian woman, someone who might not know him – and therefore not detest him – he's just not appealing. He's not muscular, he's thin and weedy. He doesn't go on dangerous missions, and he doesn't have a sparkling personality.
Not to mention it's only polite when you're on a date with someone to take off your damn sunglasses, (a request made by more than one fed up student), and the fact that he won't is a sign of his idiosyncrasies, his not-quite-right-ness, which marks him as just another dysfunctional ninja with no social skills.
No, not even a civilian woman would want him.
And he would rather die than succumb to an arranged marriage.
But if he doesn't get married he'll disappoint his father permanently, and if he manages to do that, well, then he may as well commit suicide, no matter how great a tutor he is.