The amount of DNA you have is not infinite. You cannot share significant genealogical amounts of DNA with every far-flung distant cousin you have. Humans have a lot of DNA, but the amount stays the same with every generation. You don’t get every “drop of DNA” every one of your ancestors had. There is a 69.8% chance that you and a 5th cousin have no detectable DNA relationship. That does not mean you and that 5th cousin do not have the same ancestor.
You just don’t have a big enough DNA chunk to prove it.