Surely you can understand that the worst fears a parent has are, that their daughter hooks up with a loser, with no future other than jail, and has babies by him.
I don't have any advice what you can do to change your parents minds about such a guy, but I do advise you to make sure until he has proven himself for a lot longer than he has, please don't get pregnant.
Both Our Parents Are Expecting GrandChildren . I Was Thinking It Might Be Him , But A While Back I Had Sex With One Other Guy Unprotected & Again I Didn't Get Pregnant. & I've Never Even Missed A Period . So Is It Just Me?
Whether you can or can't, that's for a doctor to say, but unless he does better than stay out of trouble, such as with his grades, and behavior and job prospects, I doubt they see him as anything but a loser. You can also explain why you both are irresponsible by having unprotected sex, and you even having sex with another guy, and worrying how you didn't get pregnant.
Maybe your parents see you as being as irresponsible as this fellow is, and don't want you barefoot, and broke in a dinky trailer, and on welfare while he is in jail, for the rest of your life.
I think if you showed them you can do better, and so can he, with positive actions, toward your own futures, they may change their minds, but if they see what I and others see, they will never be happy with your choices.
You can't expect them to be happy with the choices you have made so far, and seeing what you are unable to see.