There is one notable example that I'm aware of, but it really is a cognitive deficiency.

The contrapositive is a rule that says that "A => B" is the same as "not B => not A". This is very confusing to people, and few can follow verbally why it works.

But here is a fun experiment. People are presented with a selection of envelopes, all face down, and are asked to verify the fact that, "All unstamped envelopes are small." They immediately begin turning over the large envelopes, then have trouble explaining their (correct) reasoning!

Here is a correct implication process for their actions.

"All unstamped envelopes are small." => "unstamped envelope => small envelope" => "not small envelope => not unstamped" => "large envelope => stamped"

At which point it is easier to just check the large envelopes!