If I'm in the unfortunate situation of having to deal with an agent for a booking, I'll generally have the flight numbers at hand and reference them during the entire conversation. If they ever bring up where I'm going to/from I'll just say, "I've got no idea those are the flights I need!" That being said, your experience is unacceptable. While you may have been a bit snide, that was due to being frustrated with having to repeat yourself several times. HUCA seems to be the best way to get good customer service at UA, it's sad but true! I've had some agents who I didn't have to say a word, they knew exactly what's going on and did it for me. I've also had others who didn't understand the *A rules for rebooking and I had to cite the page # and paragraph from them to double check.
Safe Travels,
James