What is the purpose of an "answering service" for a doctor's office?

I called my doctor’s office this morning, with the intention of rescheduling an appointment. I had intended to leave a message, assuming I would get a machine.
Instead, a woman answered, which surprised me. I said “Hi, uh,” since I was caught offguard. Before I could get past “uh,” she blurted “they’ll be open at 9” and hung up.

I’d be lying if I said I wasn’t pissed. She essentially hung up on me before I even had a chance to speak. Even if the answering service is for emergencies only, she didn’t even give me a chance to say anything. What is the point of an answering service? Would I be out of line to complain? I am really mad about this.