Right, if you're a mechanical engineer and tell people you're a software engineer, they'll get upset when you can't engineer software.

There's no irony here sadly. You're just engaging in the worst sort of pedantry: attempting to be pedantic about something you're wrong about.

Without throwing around insults that are out of place on HN, I think the GP's position is fairly straightforward, at least as I understand it.

Software developers have a tendency to call themselves "engineers" based loosely on what they do (software engineering, or at least development) rather than based on them holding an engineering degree and/or professional designation. I'm neither a software dev nor an engineer, and I initially found it confusing when I'd come to a forum like this and see people say "I'm a software engineer" or "I work as a software engineer for X" without actually having any of the aforementioned credentials.

In contrast, I don't think people are so blase about using the term "engineer" casually in other contexts, or even other areas of engineering. Folks calling themselves mechanical engineers, or electrical engineers...actually are engineers. As for the example you gave of a "car doctor", it is evident that people might use the term "doctor" in such a way as to show they're not actually doctors, which is not the case in the present context. I don't see mechanics referring to themselves as just doctors, or describing what they do with cars as medicine.