exam regrade request advice

hello! I recently got my score back for a final (intro to logic design) and I got a score that would land me a good grade in the course overall, so of course I was ecstatic because my hard work finally paid off. However, they updated everyone’s scores an hour later because the answer key for a question was wrong, and my grade ended up dropping 5% (does not get me the grade I want). I looked at the question, and I feel very conflicted about it because when I was taking the exam, I used the exact method taught in lecture for it (when I say exact, I mean exactly what the lecture slide did because it was on my note sheet), but when I double-checked my answer, something was not adding up. However, I let it be because I implemented exactly what I learned in lecture, so why should I question it? I assumed I messed up while I was double checking my work instead. It turns out that I was in fact right to question it because it did end up being wrong. But, since the original answer key matched exactly what I had before (this was a written response, btw), that means someone on the teaching team had the exact same line of thinking as me, right?

So, TLDR, I want to request a regrade because even though I do understand why the correct answer is correct, I just don’t think it’s fair that what I was taught in lecture was essentially not explained correctly, which in turn affected my score and will affect my grade in the class, if that makes sense. However, I do not want my professor thinking that I’m insulting his teaching because he is honestly the best professor I’ve ever had and has made this class so enjoyable. He just forgot to mention one small detail that is actually very important but easy to overlook I think. I also applied to be a TA for this course, and I don’t want this to affect my chances. But I really, really want the A in this class.

what would the best course of action be?