How many times have you tried to explain the Earth Moon system and their orbital dynamics?
The Earth and Moon orbit around each other at the point of equal mass or the Barycenter. Any system that has moving mass in balance with another has a center of mass. The Solar System has such a center. The Moon appears to orbit the Earth but in truth they both orbit the same center of mass. The effect is a bit difficult to observe as the center is below the surface of the Earth so the movement is slight compared to the Moon. It is the same with any planet or star that has bodies orbiting.
Check out this ESA short that has an excellent demonstration of just this effect.