The conclusion doesn’t necessarily follow as a matter of logic, but it would not be illogical to arrive at an opinion based on the argument as a matter of judgment.
The OP asked if example one was a logical fallacy: it isn’t. It may well be an unpersuasive argument in any given case, but it isn’t a logical fallacy.
ISTM you are taking person two’s comment as “your argument is necessarily as a matter of logic wrong, since not all x leads to y.” You are reading too much into it. They may well simply mean “In my opinion, given that not all x leads to y, response z is inappropriate”.