They say that every atom in your body is replaced every ten years, but that doesn't make you a new person, since the atoms don't replace themselves all at once.
It's like making an arrangement of tiles on a mural and slowly replacing the tiles with identical ones. The tiles will eventually be all replaced, but as long as there is flow you wouldn't consider it a new mural.
Our bodies are not defined by the specific parts, having specific molecules that were there before. It is the whole. As long as it continuously exists (and it does) even if it needs to replace its cells and molecules every now and then it doesn't matter. Even if not a single molecule is the same the body is still the same body just like the United States doesn't have a single person living in it that lived there in the first place but it's still the United States.
I do not think it is dumb, but it is far from complete. Consider all the information that is missing from the argument.
1) What is the relationship between the "we" in "...We are not our bodies" and the "ourselves" in"...Our bodies replace ourselves..."? This rides the edge of equivocation, and at the very least indicates that you are not being very careful about framing your argument strongly.
2) Is there a relationship between the real self and the body, and if so, what is it? Are we exploring a concept like the soul or other non-material concept, or are we looking at a self-aware physical process?
3) I think there is an implication that you do not state that is something like, ...Yet we have a continuation of consciousness and memory that transcends a single iteration of the physical change." (Forgive me for putting words in your mouth, especially if I am wrong.)
There is a lot of room for refining and supporting the argument, but it is based on a reasonably impressive insight.