Quarrel with
Definition 1 of 2
Pro Tip 1/3Emotionally Charged
Often implies strong emotions or anger during an argument. 
The brothers would often quarrel with each other over family matters.
Pro Tip 2/3Personal Conflict
Usually involves a direct, face-to-face dispute between people. 
She didn't want to quarrel with her friend in public.
Pro Tip 3/3Not Physical
Refers to verbal disagreements, not physical fights. 
Despite their loud voices, the quarrel with the neighbors was not a physical altercation.