For example while dogs have a much shorter lifespan than humans they seem to face all the same age-related declines humans face. This holds for animals close to or exceeding our mass as well. If different parts of the body wore out simply due to e.g. mechanical stress, you would expect e.g. dog joints to be perfectly healthy after 15 years since they are biologically very similar to human joints, when in fact dogs tend to still have arthritic and otherwise fragile joints at 15 (or earlier).
Everything declining together, just on different timetables in different animals, seems to suggest that aging is controlled by either a single mechanism or some interwoven set of mechanisms that cause everything to fail at the same time, rather than individual parts failing because "they wear out." If you could target that mechanism(s) then maybe you can make humans live as long as e.g. tortoises. But of course we haven't confirmed that such things exist, but the above is at least some motivation for why they might exist.