Just removed water heater to replace. Turned off water to water heater and turned water on to rest of house-cold water. Now have cold water why when the cold water valve is turned on water is coming out of pipe that would have the hot water leaving the hot water tank. Decent flow from this pipe not huge pressure but enough to fill a five gallon pale in a few minutes. Why would the water seem to be going in the wrong direction and even come from this pipe at all?

Because you opened a single handle faucet somewhere such as a shower valve. When you opened single lever valve and there is no pressure on the hot water side, the cold water will not only come out the spout but will flow back through the hot water pipe.

If I understand correctly what you are saying, this will happen if you have single handle faucet or faucets when you open them the water will cross through to the hot side.

Harold nailed it. Install 3/4" plug ( or cap ) on hot water line at the water heater and you can continue using cold water w/o leaks. Milo