Sorry I RANT in this and it looses coherence at some point:

Ok so first of something that I have noticed in life. No research I can think to back me up but Years of observation of my father, brother, husband, male relatives vs mother, myself, female relatives. This is generalizations and not fact just from my experience

Men do not either notice or think that things need to be done right away. Men will leave anything to the next day and the next day and so on and so forth. I don't believe this is a conscious choice/decision. I think they are just wired to have "blinders" up around their eyes and ears. (example being if a baby cries they will sit there until mom handles it or until they "feel like it is bad enough"; open a bag of chips and either leave it open to stale or empty on the coffee table, stomp around house in dirty shoes and leave trail to be stepped in by others, etc.) Or they will do it and do it to such a subpar level that it is harder to redo it then if they would have just left it alone. This is where the term weaponized incompetence comes from.

Women notice and jump to handle everything. It bothers us to see something not being taken care of immediately. Like stresses us fully. (example, baby cries we jump, we throw everything away as we go, we take shoes off to make sure we do not tract stuff through home, etc.)

Now, what is concerning is that he is pushing the blame for his lack of initiative off on you having initiative. While like I said above men seem to me at least have not domestic initiative built in to their dna, they can infact change that. I always coin it as "if your job said you had to have the work place spotless (like lick the floor and not get nothing in your mouth clean) they would 100% do it with out having to be told or reminded. So why is the home different." Your BF knows that you will infact handle it all so he lets you. It is not that "you get to it first" it is that he doesn't want to and wouldn't do it but his excuse for his lack of initiative is that you did it first. This is showing he is 100% aware of the fact that you are doing everything. He saw what ever it is that you handled first. He knew. Or else the response would be a clueless one of not even realizing that was a thing.

When you actually "listen" to what people say to you it is very telling of the fact that they know exactly what they are doing.