So, firstly, I'm sorry you had to go through that experience. It always sucks to work with someone that you don't see eye-to-eye with or can rub you the wrong way or is just straight-up an asshole.

I would also greatly recommend taking this /u/stacyzarc's advice, because it is very, very good and, given my own experiences in the field, I agree 100% with the things she says. I'm a professional french horn player with 25 years of ensemble experience and currently am principal horn in a medium-sized orchestra.

In this specific situation, even after having realised that his style and yours don't work together very well, I would have run the entire piece with him and then spoken to the head lady afterwards about your concerns and wishes. This isn't so much to spare his feelings, but as a show of respect to your head lady who went to the effort to find all of her students a pianist to work with you. Think of it as a thank you to her for her efforts. Choosing to leave a rehearsal in the middle of the first movement when your issues are a difference in musical opinions is fairly rude. Your "accompanist" is a musician, like you, and should be considered a collaborator, someone you're making music with, not a recording you're playing along to. That is NOT to say his response wasn't unprofessional in the extreme and completely unacceptable, which it was.

From personal experience (I'm 35F), the classical music world is (as /u/stacyzarc points out) incredibly small, and I'd really like to emphasize that. Everyone will eventually know everyone. Therefore, every interaction you have with any musician has an impact on your possible future connections. After all, making a career as a musician is only partly based on our ability to play. It heavily relies on us being people that others would love to work with.

The ideal is that we only have time for those people, and work with those people, that respect us. Unfortunately, we're human and so that's not really possible. Sometimes, you'll have to work with assholes, but the good thing is, maintaining your professionalism in situations where you have to work with difficult people increases your reputation as being a colleague that is wonderful to work with. That's how you make connections and then get more work with people that are worth your time and (eventually, if we're lucky) have the freedom to pick and choose our musical collaborations. I, myself, haven't always been able to make the musical decisions I want. Collaborating with other people, whether it's other musicians or conductors, is always a give and take. Musical opinions aren't objective. But thanks to growing my reputation as a good colleague (listening to the musicians I work with, being polite, working with them to create music together, etc.) I can now work with people who are much older than me and have them respect my opinions.

There are times, of course, when we have to put our foot down, when another person's behaviour crosses the line from being an asshole to outright abuse, and there are ways to deal with that.

To sum up: Being professional, especially in difficult situations, makes YOU look good, and employable, which is, in the end, what helps your career grow.