[...] you can always reverse (a process) to determine [...] There is a precondition - constant non-zero Jacobian - to the inverse existing and the inverse is c

[...] you can always reverse (a process) to determine [...] There is a precondition - constant non-zero Jacobian - to the inverse existing and the inverse is claimed to be of a specific kind - polynomial. The counter example satisfies the precondition and by mapping two different inputs to the same output makes any inverse impossible, including polynomial ones. But maybe that is already ELI7.