The person who feels cornered may defend a weaker position more fiercely than they actually believe it.

Ferocity is often about position rather than belief. Once someone feels trapped, retreating starts to look like humiliation, so they dig into an argument they were only half holding and defend it far past the point of conviction. You can be right and still make agreement impossible by leaving no dignified exit.

To move someone, give them a way to do it without losing face. Concede a real point first, or name the part of their view you find reasonable. And when you notice yourself defending something with unusual heat, check whether you believe it or are simply cornered.