That is an absurd argument. The modern food chain is not carbon neutral [0].
If I start running to work, I have to consume more food. If I have a vegan diet I am eating the direct result of photosynthesis. That is, we could imagine the embodied carbon of my apple resulted directly from my previous exhalation of CO2. I do not dispute that some part of the 'life cycle of food' is a closed loop in this regard.
Yet I can't just 'eat an apple'. I also require someone to grow the apple (with fertilizer and its GHG emitting production chain), protect it (likely with pesticides), clean and package, transport, store and sell the apple. By the time I chew into the apple I have already contributed to the demand of GHG emitting processes.
So if you want to rigorously compare scooters with walking, running or riding a horse (all which affect quantity of food consumed), you need to take into account the carbon footprint of food. Just as when you look at GHG emissions of fuel, you don't just look at its combustion - you look at the supply chain.
If you only look at where carbon is added (e.g. fossil fuel combustion) or removed (e.g. carbon forest sinks) from the cycle, you miss out on learning about how individual actions or choices affect the rate at which addition or subtraction occurs.
[0] - https://www.researchgate.net/profile/Henk_Westhoek/publicati...