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.
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 arbitrary size.
> Furthermore [this doesn't scale].
Precisely.
https://en.wikipedia.org/wiki/Toffoli_gate has better details.