[Tainnor]

Gödel's proof is an example of deductive reasoning. It falls apart if you don't accept its axioms.

The case for climate change, or for relativity, is made inductively, by empirical observation.

The two cases are not remotely comparable.

[User23]

Funny you should say that on account of it’s well known that deduction is never wrong and induction sometimes is.

[Tainnor]

A proper deductive argument that contains no errors will be valid, but it won't necessarily be sound if the premises are incorrect. In that sense deduction can most certainly be "wrong".