Very cute.
OK the person who is lifting themselves up must exert a force down through their feet in order to lift upwards. However, the force of the person pushing down and the force of them pushing up will be equal (Newton's 3rd Law - for every action there is an equal and opposite reaction). There is another force pulling down on this person - gravity.
If Pull up = P, then Push down = P
Therefore, vector addition of forces (with up being the positive direction and down being negative):
Fresultant = P - P - mg
= - mg (or mg DOWN)
Therefore, resultant force is downwards in the order of the weight of the person, and so a person cannot pull themselves up by their own shoestrings.
:rofl: