Today I opened Health on my iPhone 6 and I realized that it is counting my steps.
However I never enabled this functionality.
Is there a way to disable it?
It's not a feature that you need to enable. The co-processor starts tracking when you switch on your phone. To answer your question, Health app does not track your steps, it merely only shows you the data that is fed from the co-processor and other health related apps. I'm afraid it's something which cannot be switched off.
Some developers over at the jailbreak community have tried to disable it - it's worth taking a look if you're interested in that sort of solution.