I think the question is a bit broad. Do you mean stretching too far, or stretching too often, or holding the stretches too long?
Broadly speaking I agreed with Karin here.
Aristotle talked about the golden mean“. for example self starvation is bad, as is gluttony. The same is true with the stability/mobility equation. Even in yoga, which a lot of people equate with ‘stretching’ the discipline is as concerned with strength and stability as it is with flexibility. There will always be those who are attracted to the extremes (what I call the Xtreme Goldfish phenomenon), but health and wellness generally rides between those extremes.