Two experienced users, both good contributors at times, just can't get along. Every time they interact in any way, sparks fly. Acrimonious comments pile up, distracting everyone from the actual questions being answered. Tit-for-tat flags and votes accumulate. Passive-aggressive meta posts ruin your buzz. You suspect the moderators on other sites are talking about you behind your back, clucking like so many biddy hens about your misfortune...
What do you do about it?
When answering, candidates should address how their responses change (if they do) if the two have a privilege imbalance, for example if one has a diamond (mod or staff) that allows him to make unilateral decisions (delete, close, flag rejection, etc).