For every action there is an equal and opposite reaction.
So, when picking something up, you are able to pick something up because there is an opposite downwards force into the ground thanks to gravity. For two people to pick each other up at the same time, this opposite reaction does not exist and therefore it’s impossible in Earth’s gravity environment.
In essence, this has all got to do with Newton’s third law that states there is always an equal and opposite reaction.
So for example when person A lifts person B Person A experiences a downwards force of the same sizes as he is using to lift person B with. This is the same reason why guns have recoil when shot.
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