Lets distinguish 'rotation' into 'spin' (rotating around itself), and 'orbit' (orbiting around another object). The orbital motion is due to gravity. The 'centrifugal force' (instead of 'kinetic energy' of rotation, per se) is balanced by the 'gravitational force' .
The spin of an object doesn't need an external force (gravity from another object) to balance it out. The spin is maintained by internal forces: if we were talking about a spinning tire, the internal force would be the elasticity/cohesion of the material; in the case of the spinning earth/moon, its the internal gravity of the object upon itself.
"In a geocentric reference frame, the moon [orbits] around the Earth." And Earth's gravity holds it there. The moon spins very slowly, (once a month) and is kept together by its internal gravity.
In a lunocentric (?) reference frame, the earth orbits around the Moon. And the Moon's gravity holds it there. The earth spins quickly (once a day), and is kept together by its internal gravity.
: 'Energy' and 'forces' (i.e. 'interactions') are different things, so we don't like to say they directly counteract each-other. The 'energy' of the orbit, results from the gravitational force; but it's the centrifugal force (which is observed in a rotating reference frame) which is counteracted (balanced) by gravity.