Yes, and it pisses Izuku (and someone else) off!

"...tell me, have you ever heard of Quirk Marriages?" Todoroki finally asked Izuku, who paused, and shook his head.

"Can't say I have, though... based on the name, I'm guessing they're arranged marriages meant for people with Quirks that complement each other somehow or another?" Izuku reasoned, and Todoroki nodded.

"You're correct. You already knew that my father is the Number 2 Hero, Endeavor," Todoroki nodded. "And he was... obessed with becoming the Number 1 Hero for the longest time, but certain limitations to his Quirk ensured that he could never surpass All Might. So ultimately, he gave up on doing so. Instead, he decided to ensure his offspring would. He specifically married my mother for her ice Quirk, with the intent of having a child with a Quirk that could compensate for the weaknesses of his."

He then hesitated again, before finally going into detail, about how when he had finally been born, Endeavor had become abusive, training Todoroki harshly, while neglecting his siblings. It had all driven his mother insane, and in a fit of distress, she had lashed out and ended up flinging boiling water on Todoroki, which is what had left his face scarred. Todoroki blamed his father for driving her to that point, and Endeavor had then put her in a mental institute, and left her to rot there.

Izuku... was angered by this. For a parent to not see their own child as their child, but instead their weapon, was infuriating to him. Still, he had to ask, "Why are you telling me this?"

"Because, Midoriya, I want you to understand why you won't beat me again today," Todoroki replied firmly. "I do intend to become the Number One Hero... but I'm going to do it without using my Father's Quirk. I'll do it with my mother's and my mother's alone."

"...it's not your Father's Quirk though. It's yours," Izuku replied, making Todoroki blink. "You have every right to want to spite him, don't get me wrong, but you can't make it to being the Number 1 Hero while holding back. That's a position you can only get while trying your hardest. If your resentment for him is holding you back, then he still has some kind of hold over you, even if it's not the kind of hold he wants."

"...you don't know what you're talking about," Todoroki finally said, before walking past Izuku. Unbeknownst to either of them, Bakugo was around the corner, having been about to pass by, before overhearing enough of the conversation to decide to listen in. And despite his general attitude towards people, he was just as sickened by what he heard as Izuku was, though also angry that Todoroki was fixated on beating Izuku, and not him. He stormed off, resolving that, brackets allowing, he would beat both of them today.