Loopholes

Midoriya Izuku never received All Might's quirk, reason being he had already moved on from his goal of applying for Yuuei's hero course. Due to rules that have been set in place, without a quirk, there is no legitimate way for Midoriya to become a hero.

However, the drive to help people still resides in Midoriya's body. Throw a mild case of pyromania, an incredible ability to analyze quirks, and the skill to create into the mix, and the result is one Midoriya who's now aiming to apply to become a support course student.

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But who ever said that he gave up on trying to be a hero?