Why is thesystem pushing coolant out of overflow hose

Sounds like you have a blown head gasket. You can try a head gasket sealer such as Bars Leak which I would recommend trying but no guarantee and if that does not work head gasket needs to be replaced.

If you over filled the coolant there would be some over flow for a while when your car is warm.

that last answer is probably right but you also may have a bad radiator cap and is the cheaper quick easy test if you dont have the right tools to test the cap

Chevy cavalier's have an expansion cooling system meaning there is no overflow hose that drains out side of the system. Any overflow is sent through a valve in the cap on the expansion tank through a small hose and back into the radiator. If fluid is leaking outside of the system I would check for cracks in the hose especially where it connects to the tank. If there is an actual hose hanging of the expansion tank with no connection at the other end this is not right for this type of cooling system. All my research says all Chevy cavaliers have a closed cooling system with expansion tank no overflow hose. I could be wrong or it could be a different system but I would definitely check my owners manual first.

Gmastired my 2002 cavalier has a hose right at the cap on the bucket and our old Sunfire was identical.

Gmastired, my 1998 Chevy Cavalier is like you explained. But you know where you put the top on the over floa? That is where my cooling fluid is coming back out of....when it gets warm... please help !!!

Buy a new cap. Even if it looks okay they are cheap pieces of crap and wear out quickly.