He had arachnophobia

Izuku was your boyfriend..you knew about eachother almost everything! He just didn't tell you he has arachnophobia because he thought he wouldn't look "man enough". So he just kept it as a secret.

But that wasn't a good idea to do so!

Izuku was inside his dorm..you were just coming to his dorm but before that— Izuku rushed from the dorm into you immediately. He was shivering slightly.

"Kill that." Izuku pointed at a spider..he went to your arms. Clearly afraid of that shit.