Pat - I've worked in the Library & Info areas of Government agencies for the best part of 33 years (worse part??) & have come to the theory that there are folks who KNOW everyone is rude so they snap & snarl & swear & demand & are never surprised when someone snarls back. Naturally they never realise that their attitude is the cause of all their problems.
Being polite to them is they only way to survive. Naturally they can't see you gesturing or summoning colleagues to have a listen at this nutter, or patting your teddy bear, reading a good book or whatever you need to do to survive the call. Descending to their level is becoming just like them.
My favourite call happened several decades ago - this twit was going on about being a taxpayer & demanding to get what he wanted & I'm only a public servant therefore as he is a taxpayer etc. So I let him rave on. When he finally finished I stayed silent - till eventually the silence was too much for him & he had to enquire hesitantly
"Uh, are you still there?"
"Yes, is there anything else you want" I said politely & nicely & kindly & sweetly.
"Thankyou for calling" I said even more politely etc.
"Uh, good bye"
and I hang up politely. AND I'D WON!! so I danced around, crowing to everyone in a very juvenile fashion!
Of course I done't behave like that these days. Tho one day a few years ago I did yell back at an idiot, thus proving I'm not perfect & really shocking my younger colleagues!!
After a "difficult client" you do need to debrief (2 modern business terms in one sentance) & it really helps to have supportive folks around you.