To be fair, pride isn't what made Salvin fall. He would have surely chosen to retreat if he knew he didn't have a chance against Litori. He would have escaped for his life. Then return with a larger amount of phantom weapons. But he didn't know about Litori's trump card. It is ignorance that doomed him. Ignorance is not a thing that Salvini struggles with. It is a tool to bring about her expected end.
He knew that if her domain were larger then he might lose. That misinformation gave him the confidence of victory since he can't control his emotions. Then there's her saying that he should be careful of her taking control of his phantom weapons.
