edit: I don't understand why my comment is so controversial. We are all subject to the laws of thermodynamics. DNA, proteins, cells, and body structe is basically matter in low entropic state. Its interaction with the environment will inevitably lead damage or erosion of said structures, a basic process of entropy increasing in the system. Nobody is exempt from this process.
That the engine doesn't work forever may very well have a thermodynamic expression, but "because of entropy" is basically missing the point.
As long as you are gaining weight/height, you should be decreasing the entropy of the system around you. Your body’s entropy should be increasing in absolute terms but staying the same/decreasing as a percentage of your overall body.
In the context of a human body, the coded information in our DNA, the structured cell walls in our body, are states of matter that is low in entropy. They will eventually get damaged due to interactions with other matter around us. The damage in this case will manifest itself as "aging".
Yes, human bodies by default incur damage and stop functioning within ~100 years. But what prevents that damage from being repaired, other than our ignorance? Are you/they actually claiming it literally violates the laws of physics to repair a human body? Because if not, I reject the appeal to entropy. Entropy is a very specific thing; it is not a generic stand-in for "stuff must break down".