The torrent of words calmed when Valiant placed a hand on the boy's shoulder. "Well, young Midoriya, I'd like to get to know you a bit and then we can decide if my dojo would be a good fit for you."
Gesturing for the two to follow him, Valiant led the way to a small office, where the former pro hero listened to Izuku stammer about himself, offering complete, if somewhat rambling answers. Overall, though, Valiant couldn't help but be impressed with this boy's character and determination, as well as his mind. 
"I would love to take you on as one of my students, young Midoriya. For training purposes, though, I need to know what your quirk is," Valiant said, absentmindedly beginning paperwork for the boy. 
At the man's words though, both Midoriya's froze in place, afraid of the reaction their answer would provoke. In a small, quivering voice, Izuku nearly whispered, "I'm quirkless." 
Valiant's years of training as a pro had taught the man how to disguise his emotions, so there was no surprise on his face when Izuku spoke up. He had fully expected a mental quirk of some kind with how perceptive the child was, but if anything he was more  intrigued after learning that Izuku was quirkless. 
Clearing his throat, he said, "That makes my job easier. It can be difficult to find a fighting style to suit a certain quirk, but this means that you have an entire world of possibilities before you." 
It warmed Valiant's heart to see his newest student straighten up, beaming brighter that the sun itself. But the image of Izuku's tragic resignation to his fate made the retired pro feel like his heart was in a vice grip, squeezing tighter than he thought possible. 
When a knock sounded at the door, Valiant abruptly realized what time it was. His interview with Midoriya had taken longer than necessary, and now his next student was here for his private lesson. 
Rising from his seat, Valiant opened the door to his office. "thank you for being patient, Ojiro. I would like you to meet my newest student, Midoriya Izuku."
Izuku craned his neck to see the boy around the teacher, a blond boy that looked overwhelmingly kind. He would have been a bit plain looking if it weren't for his massive tail. He immediately smiled at Izuku. "It's nice to meet you, Midoriya. Is this your first time in martial arts?" At Izuku's nod, the boy said, "Well, I look forward to sparring with you." 
The smaller boy nodded, inwardly lamenting that Ojiro would likely refuse to talk to him once he found out that Izuku was quirkless. Until that day, however, he planned to bask in the boy's kindness as long as it lasted. 
Soon enough, Izuku's martial arts lessons became a bright spot in his weeks. Valiant's quirk was a slight enhancement of his physical abilities. He was stronger, more flexible and dexterous than the average human being, but it was just barely beyond what a quirkless person could achieve. Valiant had never been in the top few heroes, but he had been successful, and Izuku had always respected the man. (He had also followed Valiant's hero career closely, as the man was as close to a quirkless hero as Izuku had ever found.) 
Just as Izuku respected his teacher, the man grew to respect the boy in return. He had instantly been drawn in by how bright and genuine Midoriya was. However Valiant was consistently impressed by how the boy managed to excel at everything he was shown, not through some innate ability, but because the boy tirelessly practiced everything he was shown. 
Midoriya had a whole host of others who he impressed as well. In order to give his students variety, Valiant often brought in other instructors to introduce different fighting styles. Many of these were pro heroes who Valiant had helped train years ago, and almost every instructor asked about Midoriya. Gunhead was especially impressed by the boy. That was not to mention the other students, who were inspired by the boy's determination and drawn in by his kindness.