Re: "The goal is not to throw"
I can be regularly quoted as saying "who cares if I do kotegaeshi". When I read "the goal is not to throw", it struck the same chord with me. When "using" Aikido; that is to say when an Aikidoka is forced to defend himself. He shouldn't care about throwing, or applying any technique. He should only worry himself with returning the situation to a calm state, that is to say bringing the conflict back into accord. Maybe one could use a throw to do this, or a kotegaeshi, but that's not the goal. The goal is to make the conflict come back to a harmonious state.
When training, don't work to master throws, work to resolve conflict. Strong awareness, and a calm mind do this much better than any throw (or kotegaeshi), ever could.