WARNING: The following contains spoilers for Season 5, Episode 20 of My Hero Academia, "My Villain Academia," now streaming on Funimation, Crunchyroll and Hulu.
Tomura Shigaraki has been My Hero Academia's villain in the shadows for most of the series' run. He orchestrated the attack on USJ, Bakugo's kidnapping and several Nomu attacks on public spaces. As head of the League of Villains, his evil nature has never been in question but exactly why he's evil is less understood... until now.
Shigaraki's relationship with his mentor and series archvillain, All For One was made apparent early on in My Hero Academia but the depth of their relationship hadn't been explored. Episode 20 of Season 5 finally provides a backstory for how the two met, revealing that they go further back than anyone would have imagined.
It took Dr. Daruma Ujiko asking Shigaraki why the upcoming symbol of evil was worth helping for him to finally divulge his past in the episode. As it turns out, Shigaraki's earliest memories are of All For One. Shigaraki describes how the villain boss rescued him from a life on the streets, with his sole knowledge of how he'd ended up there being his new patron's explanation of his past. According to All For One, Shigaraki suddenly manifested his Decay Quirk, a mutation unique to him, and in his confusion at its appearance, killed his entire family. A chilling origin, albeit fitting for a villain like him.
Shigaraki's unfortunate background isn't the cause of his evil inclinations, though. As much as being completely socialized and educated by All For One fostered his homicidal tendencies, Shigaraki also mentions that the anger he feels was always within him. In his monologue to Ujiko, he describes his past before All For One as just fragmented images that somehow continued to fill him with a rage he could not understand. He goes on to call his anger a weight that would never go away even if he managed to achieve any of his ambitions. This anger isn't directed at any one thing in particular, leading Shigaraki to believe that he hates everything. Therein lies his true danger.
Because of his perceived hatred of everything, Shigaraki's conclusion was to destroy everything. Save for all the members of the League he holds dear, Shigaraki's current mission is to tear down every system and structure in place since none of them could serve to quell his rage. That means that unlike other villains -- who at least have some constructive goal they hope to achieve -- Shigaraki is a being driven by pure destruction. For that reason, his apathy towards everything makes him especially dangerous because there's nothing that exists that could be used as leverage against him.
The one setback he would have encountered in his journey in My Hero Academia seems well on its way to getting solved too. After hearing Shigaraki's speech, Dr. Ujiko agrees to help him out. With the doctor's help, Shigaraki stands to receive power on par with the toughest of Nomus while still retaining all sense of self. His newfound strength would make his goal of destruction even easier, too, as should his wildest dreams be realized, there isn't a hero in existence currently who could defeat him.
As to whether All For One approves of his current plan, it's hard to say. Since adopting Shigaraki, he's encouraged the young boy to think for himself, training him to make increasingly more difficult decisions and shielding him from the consequences as best as he could. Hearing that Shigaraki's finally working towards a set goal would please All For One, but total destruction seems at odds with his previous ambitions. After all, if everything is destroyed, what would be left for All For One to rule?