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Obviously we are talking past each other. What do you mean "by launching
upwards"? I imagine you mean pushing against something, such as a
platform. Then (by the 3rd law) there is a force on your body from
outside your body. It is this force that allows your center of mass to
move. If you are free floating in space, you CANNOT move your center of
mass. This is surely elementary.
When you "launch upwards" by pushing against something, that something
"launches downwards", the CM of the whole system does not move.
J. EPstein