> any Boolean function can be computed reversibly This only holds because the system returns its raw (a, b) inputs unchanged. It doesn't seem like a useful property. Of course we can "reverse any function" if we store the inputs! Reversing here just means yielding back the inputs.
> Reversing here just means yielding back the inputs. Not quite I think - the example gate they give has (a,b,c) as input and it doesn't return c. So it's not yielding all the inputs back. Furthermore: if you always returned all the inputs, and also computed other values, the outputs from the gates would be strictly increasing in size, so you wouldn't be able to use a finite set of gates to build a computer of arbitr…
Another way to put it: each step in a reversible process must be a bijection, or "information-preserving". The naive way to do that is to return the entire input as part of the result, but that's missing the point.