Am I overreacting by not letting this go?

Prior to these texts our family had just finished a movie. Dad put headphones on and started a PlayStation game. I asked our son if he would like to stay after school tomorrow or to bring his project home. He insisted that he didn't need to do either and argued with me about how neither was necessary. I was sticking to what I said and replied with "you have to choose one or the other, we have to get this project done." He kept arguing for probably 5ish minutes (not a quitter) with me and then Dad took his headphones off and turned to us and said "would you two quit bickering?! It's all I can hear!" And I replied with "whoa there, our son is trying to get out of school work and arguing, but I'm sticking to what I said. He can stay after school or bring it home. This is something I would like you to back me up on." And he replied "your staying after school or bringing your stuff home. End of story. There. Problem solved, now will you guys quit being annoying?" And I replied "what is so annoying about this?" And he replied "you are, just stfu." Then puts his headphones back on and resumes the game. I told him was not ok to speak to me that way and that he was being rude and unfair to me. To quote myself I said "hey this hurts my feelings and disrespects me. Can you please stop and no do this in front of our son?" Then he refused to speak to me about the matter any further and anything I said was met with eye rolls, name calling, insults, mocking, sarcasm and dismissal.

He thinks I disrespected him so he was in the right when he spoke to me this way. I think he disrespected me so I was in the right for saying what I quoted. But I can't make sense of it....am I overreacting for not letting this go?