I can understand why it would matter to them, but sometimes you just can't get everything you want. Allowing outside influence like that can destroy the first steps of a marriage. If they love one another, they're just going to have to ignore that outside influence, no matter how much it hurts.
Not required by the universe, yes of course. But the girl wants her parents approval, that was made quite clear by the OP. Everything I've said has been a response to their stated dilemma which is the flack they are getting from their parents and others.
Saying "if they are in love it doesn't matter what anyone thinks" is.. well, ridiculous. They live in a world of family, friends and work and they want this relationship to fit into that world, not to say fuck you we'll do what we want.
Indeed, and if their family doesn't support them, let them go. If their friends don't support them, let them go. If their place of employment doesn't accept them, leave. It sounds cut and dried, though I realize the massive implications it would have on their lives, but it just seems such a shame that people whom the marriage doesn't harm, can be so devastating to that couple.
If I was the man I would be very worried about my job and what kind of reaction I will be getting from my colleagues since he's a teacher. If he doesn't move in with her and doesn't marry her until she's 20 he might get away with it. Otherwise he's pretty much marked himself as a teacher suspiciously attracted to teenagers. If I had a teenager in his class and heard he had married an 18 year old I would be completely freaked out and the school would be in a position of justifying this.
Since they care about their families, friends and job then clearly "it doesn't matter what anyone else thinks" is not the case.
Of course they care about their family, friends, and jobs. It's just sad they apparently have to choose. They shouldn't have to choose. It shouldn't matter. They have a right to be together if they so choose, and if a family member, a friend, or an employer cannot see that and actually tries to intervene, then what a terrible way to treat people these aforementioned groups claim to "love".