Warning! Spoilers ahead for My Hero Academia Chapter 317!
Deku not only just proved that he no longer needs All Might but he pretty much says it to his face in the latest chapter of My Hero Academia.
The shocking statement follows a series of unfortunate and rather aggravating events that seems to have greatly affected the young hero in training. It's clear by later extenuating circumstances that what transpires causes Deku to focus even more so on the task at hand than before if that is even possible, pushing him to a point where he is able to articulate to All Might that he no longer needs him. Deku, who was already in a tough predicament when he learned that All For One had set his sights on him to acquire One For All, was forced to go rogue to keep his teachers and classmates safe at school and to hopefully draw out the psychopathic villain.
Things escalated quickly when Deku learned that All For One didn't fall for their trap and instead sent the hero traitor and assassin Lady Nagant after him. While Deku obviously didn't want to be hunted by an assassin, he soon took advantage of the situation when he was able to successfully connect with and sway Lady Nagant to become a hero again. But then it happened. All For One triggered a Self-Detonation quirk that he had hidden inside of Lady Nagant to not only punish her, but to set in motion a dastardly trap that allowed him to tout his successes to Deku later on and to tarnish Lady Nagant's redemption.
All of these horrific events seemingly push Deku to the edge as he quickly defeats another one of All For One's assassins with relative ease, as revealed in chapter 317 of My Hero Academia. By the time All Might finally catches up to Deku, Deku quickly moves onward, leaving the former number-one hero behind. All Might tries to convince his successor to rest and at least eat, but Deku turns him down, saying that he's fine since he can now move at 100 percent without damaging himself, just like All Might used to during his prime: "All Might, you don't have to follow me around anymore. I'm fine on my own now ... So don't worry about me."
This is an incredible moment for Deku, but, sadly it is sullied by the darkness that now overwhelms him. Deku has always looked up to All Might as a hero and wanted to be just like him since the very beginning of My Hero Academia. So when All Might chose to pass his power to him, Deku dedicated the entirety of his life as a quirk user to ensure he could carry on All Might's legacy as the next hero of peace who could bring hope to the most hopeless just with a smile and by saying, "I am here." That moment is now finally here, but Deku doesn't have time to rejoice. Nor does he feel the need to celebrate with his hero. The only thing he can or wants to do is push himself forward to defeat All For One. It's heartbreaking and ironically tragic because the moment when Deku finally can admit that he no longer needs All Might, is when he actually needs him the most.