Yeah! I was wondering that too. Either it was a flub that they left in because it was funny, or it was a flub that they left in because they didn’t have another good take, or it’s a breadcrumb for a weird AI-takes-over-the-Enterprise season finale.
Yeah. Pike kept trying to avoid the family conflict the whole episode. Seeing the door shut on him and him trying to wave it open was comic gold. He was probably thinking, “what the hell? This is my ship!” then he just stood there looking awkward. Gold.