I looked through the comments to see if someone mentioned the order of operation. You could say it is this at a first glance, but... nope. False proofs always appear because they are generally presented with what seems to be valid math as in the example above. The mistake in this case lies in treating the infinite series 1-1+1-1+1-1+....= 0. This is the catch. Grandi’s series does not converge in the traditional sense - its partial sums just alternate between 1 and 0. You are basically manipulating the result of this and force it to 0 artificially.

This is my opinion.