Capitalist, because the inherent structure of the body and all living things is to be entropic, and to forward entropy in a more efficient way. We consume in great amounts to reduce the energy in a system, even if said process is incredibly slow in our perception of time.
We do the work for entropy, so that it can tear down the higher energy levels in the universe.
Of course, do note that things with high energy want to reduce their energy. Just how entropy works at the baseline; living things merely accelerate that in an efficient way.
Your classmate isn’t necessarily wrong but this specific question changes the context. Asking whether or not the body is capitalist or communist implies that you treat the body as a society and determine which type of society it’s more akin to. The body is only capitalist if you view it from the perspective that the body is a “business”.
In regards to the question itself, the body is closer to what everyone thinks of when they hear communism because the body attempts to sustain itself as a whole rather than each individual part working to sustain itself (from each according to his need). But that isn’t quite accurate either. The true idea of communism is a stateless, classless, moneyless society, the reason most communist societies ended up as dictatorships was because part of the outlined process to achieving communism was to install a “temporary”(lol) dictator. This is more accurately called “state socialism.”
However, you could argue that the body purely works to sustain the brain rather than to sustain itself as a whole. In that case it’d be something completely different entirely (maybe fascism).