So yesterday while me, my father and my brother were having dinner, we were talking about this family we knew and I mentioned that one of their kids had told me his mother is bisexual. My dad immediately asked if his mom had girlfriends from time to time or something to which I said no, they are happily married. My dad then asked why in the hell would these kids my age (all approximately 14-17) know their mother is bi. 
I, myself a bisexual person, was a little confused and I said I thought it was a normal thing to share, to which neither my father nor my brother agreed with.

 My father then said that in the case my mother was bi, (she is straight, so this is a hypothetical scenario) he would find it strange if she shared it with not only me and my brother, but anyone. He said he would feel insecure if his partner would tell people she’s bi (but happy with her partner and not planning on leaving him). To me it sounded like he wanted my hypothetically bi mother to pretend she’s straight just because she’s in a straight marriage, plus it also sounded like he thought a bi woman was more likely to leave him for another woman.  

I was pretty upset at this point and I said to my father that I thought this statement was kind of biphobic. Now my father knows I’m bisexual myself and he’s been extremely supportive so he did not like my accusation at all. Where I meant ‘hey, this is kind of biphobic to say and it has upset me.’ He took it as ‘I think you’re a homophobe.’ And got angry in return, saying he did not deserve that.
 
A bit of pointless discussion later I stormed off to my room as he refused to apologize, and when I said I didn’t like hearing this stuff in my own house because I hear it at school so much already, he said he would not walk on eggshells around me. I felt like I was reasonable asking him to be a little considerate, as I feel his whole standpoint kind of came from the stereotype bi people would not have ‘enough’ in one relationship.

So, AITA in this scenario? Should I have heard him out and not gotten upset or was it okay for me to be angry?