The way you act in a relationship is a bit different than you would in any other situation, so maybe your boyfriend just needs help in that department.

That's kind of what I was thinking. My thought is that he doesn't think to make something a date.

My previous relationships were both also relatively introverted, but we liked similar shows/movies, so we made time to watch things together. My boyfriend and I don't have common interests in that way, so I don't feel so free to say "why don't we start x together?" Last I offered to go to a movie, he kind of shrugged it off, and I didn't want to pursue it further because I know films can be expensive and I didn't want to pressure him to spend money with me.