Step (3) is not valid. You can't use "I would reason badly in case A" as a proof that A can't happen. At best it's an argument that, when deciding what to do, c

Step (3) is not valid. You can't use "I would reason badly in case A" as a proof that A can't happen. At best it's an argument that, when deciding what to do, case A isn't worth worrying about. But that's different from asserting case A can't have happened.