A teacher who apparently has zero knowledge of how teenagers commonly behave? Something smells off there.
In my case I felt equally embarrassed by my parents' existence and I couldn't in any way have explained why. I certainly wouldn't have wanted them anywhere near this kind of event. As an adult I now realise that it was representative of my very bad relationship with them (bad for various different reasons).
I was also unable to articulate at the time but yes, without meaning to be my father was embarrassing. He is quite clearly ND but undiagnosed because obviously there's nothing wrong with him - it's everyone else at fault. Now I can see clearly the social awkwardness, the inappropriate and bad taste comments, the failure to communicate properly with others. At the time I couldn't identify any of this clearly, I could just feel the secondhand embarassment as other people would raise their eyebrows, look unimpressed and internally brand him an idiot - none of which he could see, he just got worse and worse assuming their silence meant they agreed with his off colour remarks. Racist, misogynist, just hateful. Ask him about any of this and he'll say I'm talking rubbish. However as an adult a number of other adults have since told me how awful they think he is, which they certainly didn't tell me as a child. My mother wasn't much better, for different reasons, and always trying to overcompendate for his ineptness.
I'm not saying you're an idiot as he is, OP, but maybe there is something you're doing that your daughter is unhappy about that you don't realise. As a teenager it doesn't take much to embarrass them. I remember a friend asking me why my mother put on this weird, high voice to talk to them - the kind you'd use talking to a toddler. I wanted to die inside every time she did it. I know now that in her awkward way she was trying to be welcoming and make them feel at ease, unthreatened. However it was stupid and embarrassing and so of course I didn't want her anywhere near my school or friends.
Your options are to ask about it and hope your relationship is good enough that she will share, or accept that as a teenager she's feeling pretty awkward herself and may not be able to say and perhaps you should accept that.