I gotta ask, how old is your boyfriend? The only reason I ask is because for me anyhow, when I got married, two years later I found myself taking the approach of, the hell with feeling the need to impress others.
The way I transitioned was for 20 years I went every four weeks short and cropped. The next seven I went every 6-8 weeks semi-short. The last year, I go every three months and tell my stylist to "leave it longer" after cutting it.
I'm finding that three months between haircuts is a perfect balance between "rocking the curls" and not letting it get out of control.
Keep encouraging him but don't ram it down his throat. Not that you are but you get the idea. It's just that you can't force someone to get on board.
Maybe tell him, "Curls aren't just for girls."