Izuku isn't ashamed of you, just... with him having been quirkless before, he doesn't want Kacchan to think he can bully him and you further if he knew how much you were still in Izuku's life. And Izuku's super shy and scared about telling his mom he has a boyfriend considering not many families would support. He knows his mom would most likely be fine with it... But he's still super scared. Plus he isn't sure what your family would think either!

Izuku waits outside UA's entrance gates after school, looking around frantically as he backs away from his departing friends, getting to the secluded area where all the students leave.

You eventually pop out, wrapping your arms around his neck from behind, bringing a bright smile to the boy’s face.