Question

why does a geostational satellite have to orbit around the equator

Answer 1

They are not required to, exactly, but any inclination to the orbit will cause the satellite to appear to drift back and forth from the ground. The whole point of a geostationary orbit is so the satellite appears to be in the same spot in the sky. Even so, geostationary orbits are idealized and not completely stable. Satellites placed in those orbits will drift due to several perturbations. Gravity from the Moon, other planets, solar radiation pressure, non-uniformity of the earth, etc. etc.
The reason they put them there is 2 things really. One, they are in a circular orbit so approximately are always at the same altitude. Two, the orbital period matches that of a sidereal day of the earth. When you combine these two requirements and apply Keplers laws, you find the solution is a circular orbit around the equator at an altitude of 35,786km above MSL. Again, the around the equator part is not an absolute requirement...unless you always want the satellite to appear in the same place. If you can live with a little oscillation of position in the sky, then you can have some inclination to the orbit. Most satellites in geosync orbit actually do have a slight inclination and drift in the sky (~0.1-3 degrees up and down).