He first wants to ask Izuku something, before they talk about Todoroki's Quirk!

"First, I want to ask you a question," Todoroki told Izuku, who nodded, paying rapt attention.

"Go ahead..." Izuku replied, wondering where this was going.

Todoroki stared intently at Izuku, before asking, in a dead serious tone, "Are you All Might's secret love child or something?"

Izuku stared right back at Todoroki, processing the question, before, without warning, he burst out laughing, holding his sides. In another time, he might have awkwardly denied it, while marveling that Todoroki wasn't wrong about them having essentially the same Quirk, but now? Now he was remembering the time Momo had asked him that exact same question before, right before he had told her and Ochaco about One For All and All Might's former injuries, and he couldn't help but find Todoroki asking him the same question Momo had hilarious.

Todoroki blinked. Of all the reactions he expected from Izuku, that was not one of them. His eye then twitched. "Damn it, I'm serious!" he snapped, barely restraining himself from outright yelling in indignation.

"S-sorry," Izuku gasped out, wiping a tear from his eye. "It's just... to borrow and alter an American idiom, if I had a nickel for every time someone asked me that question, I'd have two nickels. Which isn't a lot, but it's weird that it happened twice, right?" (I will be very disappointed if no one knows that reference to earn that cookie, lol. And yes, yes I WAS planning this reference from the moment I posted the chapter where Momo asked the question I knew Todoroki asked canonically. I was waiting MONTHS to get to this point! Worth it!)

"I... I see," Todoroki replied, still a little irked, but mostly mollified by the explanation.

"To answer your question though, no, I'm not," Izuku shook his head. "I just have a similar enough Quirk that I understand why someone might think that if they're observant enough."

"...fair enough," Todoroki accepted the explanation. "But that's not why I want to talk," he added. "I just had to ask to satisfy my curiosity." He then looked at his left hand. "You made me start to break a promise I had made to myself. To never use HIS Quirk in combat..."

"...his Quirk?" Izuku asked Todoroki cautiously, aware he was very likely treading on very sensitive ground. Todoroki hesitated as he gazed at Izuku, clearly debating on whether or not to elaborate.