#just a memory

Vincent was starting to question things. Whether it was because of the bullet hole in his ribs, or the blood loss, or some deep seated programing he still hadn't beaten yet, he couldn't tell. But all he could do was keep going. Even when his metal leg started to become heavier and heavier. Even when he felt like the metal arm in his left shoulder would rip out of it's socket.

The Bonus Disc:

Izuku discovered the time travel Quirk when he was a kid. He used it to save Katsuki—the first time he fell in creek (you know the canon moment) he hit his head and was badly injured, so Izuku reset the day. Only once, though, because the second time Katsuki fell he was fine, even if he did think Izuku was looking down on him.

When Izuku tried to tell others about the Quirk when he was younger, nobody believed him because time traveling Quirks, up to that point, had never been seen before. And unfortunately, he still has the extra toe joints indicative of Quirklessness, so everyone interpreted it as the Quirkless boy being desperate enough for a Quirk he would make something up.

In my notes, this Quirk is called "Memory."

Because Izuku's been so isolated, he hasn't really seen all it can do. For instance, although he can reset any day for any reason, when he resets a day for something specific to a person, that person gets drawn into the Quirk as well in a lesser way. This is why Tsuyu can sort of remember the previous loops at the end, because she was his focus.

For these people, this sort of just presents as a series of weird dreams and vague ideas. That kind of deja vu that's just slightly aggravating and not helpful.

Katsuki actually has some recollection of his first saving too, so he always somewhat believed Izuku when he said he had a Quirk, though he would never admit to it.

As canon proceeds in this universe and with this Izuku's Quirk, I imagine more people would get drawn into its effect too—but Tsuyu will always be special for being the first, and she will always be his rock.