Dabi wasn't trying to look for acknowledgement from Endeavor but acknowledgement for his existence. This is more about him look for a reason for his existence.

*dusts off the good ol’ askbox* Hiya thanks for the ask!

This statement is trying to diminish Endeavor’s role as Dabi’s motivation, and I don’t agree. 

Yes Dabi/Touya wanted acknowledgment of his existence. Whose acknowledgment did Touya want? Endeavor's. And his family's.

Everything Touya has done since his quirk started hurting him has revolved around regaining his father’s attention. He wants his father to look at him again. Touya has said so, and even Rei has said so (302). He wanted and still wants his father’s acknowledgment. He wants it so badly he has been self-harming since he was around 4 years old. He trained in secret for years to re-earn that attention, burst into literal lethal flame tears when his father didn’t show up to see him at Sekoto Peak, woke up from a coma making up an excuse as to why his father didn’t arrive and went home to see him and the rest of the family, and then decided to stay dead when he saw that the person who dominates their family - Endeavor - hadn’t changed. And now he has spent the last 10 years plotting to ruin Endeavor. Why? Because it hurt that his own father didn’t want or care about him because Touya loved HIM so much. Touya thought the love was unreciprocated. Dabi even tried to kill Shouto multiple times now - why? Because Dabi wants Endeavor to notice him for once. 

I’m not sure what else to say. Touya is just like any other kid IRL who feels like a giant disappointment to their parent. That shit stings. But, Touya wasn’t the kid who went out of their way to continue pissing off their parent by becoming the exact opposite of what their parent expected. No, Touya dug in his heels and tried incredibly hard to meet his father’s standards until he died. I’d even make the argument that he’s STILL trying to meet his father’s standards. He’s using Endeavor’s mentality that hotter flames = stronger and copying his moves. Touya is self-destructing because his father abused him, and to say that Touya doesn’t want his father’s acknowledgment ironically erases that trauma because his trauma IS being neglected, and he WANTS closure by being seen.

Look. Touya wants his dad, and the core of that feeling is love - wanting to be loved by his father via acknowledgment and allowed to show his love for his father via training and going into the same profession as him. But it was never only about heroics… it was about his relationship with his father. All Dabi has talked about since 290 is family this, family that, Endeavor, father, Shouto, Endeavor Endeavor Endeavor. 

I know it’s hard to fathom. Touya yearning for the father who abused him and the entire family is hard to stomach for some readers who suffered parental abuse and therefore can’t relate to Dabi, and I understand that and I see them. Horikoshi is writing the story, and he’s made it clear that the Todoroki family will heal and come together to FINALLY be happy - and this includes both Touya and an Endeavor who is regretful and wants to be better.