On reflection I'm very confused by that sentence. It has two parts, after the "with a few exceptions" qualification: "a crime is a thing forbidden by law" and "being forbidden by law means that it carries a punishment". Both of these seem to be definitions, and I'm not sure what sense it makes to give a definition while saying it has exceptions. The immediately following sentence said -- with no qualifications -- "If you aren't punished for it, it isn't a crime".

So I'll take your word for it that you didn't mean to assert that being forbidden by law means, by definition, carrying a punishment; but I can't see that it was unreasonable for me to think you were asserting that.

I don't think the original post is principally about the distinction between deterrent and non-deterrent punishment. It's about whether punishing institutions are there for reform, for deterrence, or because people just like punishing, with the suggestion that there's a great deal of the last of those even though it's usual to talk as if the first two are what matter.