I mean, much like agnosticism is derived from "not knowledge", "atheism" is derived from "not god". "Lack of belief (in a diety)" is the definition of atheism.
The distinction between strong and weak, sometimes called "positive" and "negative", is "belief that there is not" vs "no belief that there is". Similar to how different strengths of agnosticism express "do not know" vs "cannot know". They both lack a belief in a god. An agnostic who does not believe is a type of atheist. Since they're compatible philosophies there's no contradiction or need to choose. Like liking chocolate ice cream and liking root beer.