Every category is an infinity category, but the converse is not true. Thus, infinity categories are more general than categories. But you don't have to go that

Every category is an infinity category, but the converse is not true. Thus, infinity categories are more general than categories. But you don't have to go that far: Just remove e.g. identity morphisms from categories, and you get something that is more general than categories. It is of course another matter completely whether these structures are a useful abstraction for what you want to accomplish. I've never come across something reasonable that has arrows and associative composition, but no identities. As for infinity categories, I remain very skeptical that they abstract any problems programmers not concerned with topology (i.e. > 99%) have. So yeah, categories are a reasonable baseline from where you can build. But you can't show anything relevant and non-trivial that holds in any category. You'll need more structure, hence less generality, for that.