The man is not a rigid body. When the man extends his legs, his feet remain stationary, but his head and shoulders start moving upward. To make matters more complicated, his center-of-mass moves upward, but not as fast as his head and shoulders move.

A lot of the time, when we're doing physics, we look for ways to simplify our description of a complicated system. Center of mass is one such simplification. When we want to know, for example, the potential energy associated with the man's height above the Earth, we can use his center-of-mass instead of trying to account separately for potentially different motions of his head and his arms and his legs, etc., and we still get an answer that "works out."

If we treat the Earth as an immovable, rigid object (by far, the easiest way to understand the problem) then it probably makes sense to say that the man's legs are doing work on his own center of mass.

The man is not a rigid body. When the man extends his legs, his feet remain stationary, but his head and shoulders start moving upward. To make matters more complicated, his center-of-mass moves upward, but not as fast as his head and shoulders move.

A lot of the time, when we're doing physics, we look for ways to simplify our description of a complicated system. Center of mass is one such simplification. When we want to know, for example, the potential energy associated with the man's height above the Earth, we can use his center-of-mass instead of trying to account separately for the different motions of his head and his arms and his legs, etc., and we still get an answer that "works out."

If we treat the Earth as an immovable, rigid object (by far, the easiest way to understand the problem) then it probably makes sense to say that the man's legs are doing work on his own center of mass.