People get agitated when (1) they don't understand how a process works, (2) they don't like the answer, and of course, (3) when they feel nervous, insecure or out of control. Since hardly anyone can understand, much less control the US Postal Service, there's lots of opportunity for people to go "postal." (Which if you recall, was a term coined after more than one employee embarked on homicidal violence, ostensibly due to the stress of working there, but undoubtedly also related to inadequately-treated underlying mental health issues.)
This person probably was reacting in a not untypical way -- she didn't like the answer, couldn't or didn't want to understand, and just kept repeating her want/desire/previous position .. and was not in a frame of mind to cognitively process what she was being told. Her brain (or what passed for one) had checked out of the process. That's how an unfortunate number of people deal with cognitive dissonance (the answer doesn't agree with their previous notion) or frustration (they can't argue someone into their own position). If you happen to have any youngish cousins or siblings (say in the 2 - 3 year old range), that negotiation strategy is often their main method of dealing with lack of satisfaction with their available options. When the bullheaded stubborness (frustration) fails, they move on to tactic/strategy #2: meltdown.
Unfortunately, some of us never progress beyond those two tactics, and even for those who do, at times, frustration gets the better of us.
Hmmm, you are going to be dealing with lots of stressed out people in your future career. Maybe pick up a good book on behavior mod and start studying people's responses. Karen Pryor had a good book "Don't shoot the dog" but I seem to recall later editions took out some of the good stuff... Fixing sick animals will probably be significantly easier than dealing with whacked-out clients. Stress over sick or injured animals combined with vet fee sticker shock/inability to pay issues make irrational meltdowns in the waiting room an all too-frequent occurrence...
Who knew they could just put out some watermelon and the peas would dye themselves?