You can acknowledge the feelings of your partner and yourself without making those feelings the fuel of the argument. In my own experience, acknowledging my partner's feelings makes me immediately calmer, more-grounded, and better able to understand her POV. I imagine it works the same for most people.

If you're with someone you trust, you inherently respect his/her POV. For some, this causes disagreements to boil into violent outrages. They feel an attack on that trust. For others, they take a step back and say, 'This is someone I trust with my life. Either he/she or I am missing something somewhere.'