If she hadn't met Yagi Toshinori, based on Priest Haizawa's life trajectory, she probably wouldn't have met the person she was interested in.
It's possible that she had encountered it, but she was busy solving all kinds of troubles caused by All Might at the time, so she missed it.
As for Yagi Toshinori, he was happy that he was the only one called a "wasteful man" by the priest.
"You protect this world, and I will protect you."
"I am a hero all over the world, but I want to be your hero even more."
Purpose: I am a hero all over the world, but I want to be your own hero.