It’s one of the most closely-guarded secrets in the My Hero universe, so why did Deku tell Bakugo about his quirk?
Deku chose to tell Bakugo about his quirk because he felt bad for beating him during a class-training session. He doesn’t consider One For All to be his own yet, and he feels bad for Bakugo’s confusion over losing to Deku and his suddenly-emerged new quirk.
He doesn’t admit that his new quirk is directly from All Might until the two have an altercation a little later in the series.
Deku is honest with Bakugo about his quirk
In chapter #11, Deku approaches Bakugo after their first hero activity as classmates. Deku’s team won the competition, marking the first time that he’s ever beaten Bakugo in something before.
The two faced each other 1-on-1 during the fight. Throughout the activity, Bakugo kept hurling insults at Deku such as “Must have been fun, yeah? Tricking me this whole time,” and “Hiding that flashy quirk of yours!”
After Deku wins, he feels guilty that he beat Bakugo without using what he considers to be his own power. Despite all the years of bullying, Deku didn’t want Bakugo to feel bad that he lost him after all the confusion with Deku’s quirk “manifesting” later in life.
Deku says that he hasn’t even told his mom the secret behind One For All. He tells Bakugo that he can’t say much, but he should know his secret that his quirk was a gift from someone else.
He tries explaining to Bakugo that he can barely use his power at this state. Right now, it’s more or less useless to him. Deku says he tried to beat Bakugo with his quirk but couldn’t. He had to rely on outsmarting him, which is not how he intended his first victory against his rival to be.
Deku tells Bakugo that he’ll overcome him one day when he makes One For All his own power. This doesn’t make Bakugo feel better. He already felt bad enough that he was lagging behind in class and now he lost to Deku, of all people. Telling Bakugo didn’t seem to make much of a difference on Deku’s part. Yet, it relieves some curiosity between the two of them. Bakugo and Deku do end up becoming friends again later in the series.
So that’s the reason. Deku chooses to tell Bakugo about his quirk because he felt bad for being him during a class-training session. He doesn’t consider One For All to be his own yet. Also, he didn’t like that Bakugo was confused over where Deku’s quirk magically came from.