Don't your telomeres get shorter, your DNA gets damaged and it doesn't replicate correctly anymore? Some animals can be immortal like lobsters but face limits like their physical size can kill them when they molt enough.
Red blood cells and capillaries have roughly the same diameter leading to constant friction. Your body repairs the capillaries but, given enough time, it makes mistakes. As these mistakes pile up your circulatory system, your body's supply chain, slowly gets less efficient. This leads to every cell in your body gets the energy it needs a little later, and has to hold onto waste for a little longer.
This isn't comprehensive, though. I don't see intracellular or extracellular waste accumulation, for instance.