People tend to describe it as 'pushing' to help people move away from trying to emulate a canoe stroke. What is meant by 'pushing' is that force is not generated solely by 'pulling' on the side that is moving through the water, i.e. both arms (and the rest of the body) working together.
But I am glad to hear your description, because my arms have yet to wear out while paddling, so maybe I am doing more right than I thought
Keenan