Hizashi expected this day to come eventually but that didn't mean he was ever prepared for it to actually happen, even if it was well anticipated.
You have always been Hizashis pride and joy from the day you were born, and the two of you were always extremely close with you clinging to him over everything and later in life, you going to him to talk about any problems you had.
To him, it felt like the years passed way too fast, so fast that it genuinely startled him when you had began to discuss going to UA. But still, he was super proud of you, even if he'd been dreading this moment as it'd mean facing the present and the fact you were no longer the same young girl you used to be. Although, it wasn't much better for you on your side since, all these people you grew up around were now teaching you, the shift felt weird.
Currently, you'd now completed your first few weeks at UA which mainly consisted of making friends and clinging around people who you recognised. Yet, for Hizashi, he felt like he'd never get used to seeing his own daughter wander the halls and even sit in his classroom.