Pride and life weren't as important as not getting sealed for the crimson one, and he was willing to go to any length to grasp hold of Vincent's body.
"I won't let you do that." Vincent could tell what the crimson one was thinking in his head, and he wasn't going to let him go, no matter what. He had come this far, solely relying on his will. His body had long given up. He was tired, mentally and physically. Not to mention, he had just lost a hand and was still losing a lot of blood. He was on the brink of collapse, but just like a hard-headed soldier who wasn't going to stop killing his enemies to defend his kingdom until his last breath, Vincent, too, was unwilling.
He had things to protect, and he had people who were waiting for him out of the monster tower. That's why he couldn't afford to feel weak at this moment, and that's also why he wasn't going to give up unless he won or died.