I had an argument with my professor, and I feel like I was disrespected. Was I in the wrong?
Was I in the wrong? Was my professor in the wrong?


We are steering deep into the realm of Interpersonal.SE, but this is absolutely the wrong question to ask. There was clearly a misunderstanding. It happens. It does not matter whose "fault" it was (if anybody's, really - in most misunderstandings nobody is doing anything terribly unreasonable). They were displeased that their time was wasted, you apologized. Case closed, moving on. As you say yourself, there is no reason to escalate a tiny hiccup into an actual conflict.

One thing I suggest is to use this as a learning opportunity to improve your processes for future meetings. In your case, I strongly suggest that going forward you send a meeting invite to all participants after a date has been agreed upon (and also to check your scheduling software after sending out a scheduling link - at the very least a reasonable amount of time before the first slot you suggested).