At what point did you even become angry?

Your points are very valid. I don't see where you need to apologize. If anything, he should apologize to you because this right here:

c: "yeah, but usually I have twice-a-week therapy. for the last month and a half it's been nothing or once a week."
[long pause]
pdoc: "that felt like a slap in the face."

sounds ridiculous. You were merely pointing out a fact, right? Sounds like this guy just had a bruised ego moment. You said nothing wrong, nothing offensive, so I don't see any need to apologize.