All Might theorized about OFA causing death early for users who already had quirks, so it makes sense he would reject other candidates even if they seemed more suitable, like Mirio Deku was the perfect successor because he was quirkless and possessed a heroic instinct to save.

However, it was still a theory since he only had himself and the 4th user as examples of users who didn't die in battle. He probably felt conflicted about passing OFA to Deku since if his theory was wrong, he just sentenced Deku to a severely shortened life without telling him.

Midoriya Izuku: [is a good boy] Me:

Me on my Endeavour and Deku mentor and mentee relationship bullshit: wow thanks Deku for including Endeavour in the near and dear category, the fondness is mutual ig ???

I know people don't like the Culture Fest arc as it's relatively low stakes compared to other arcs, but Gentle Criminal was the first antagonist Deku could really sympathize with and understand, since Deku recognizes he could've become like Gentle if hadn't been so fortunate