me and him went fishing

Written down, this seems gross, of course.
But in the spoken word, many parts of speech are left unsaid and understood to have been purposely left out, making the spoken whole grammatically intact.

In the example above, the complete version is, "Me and him; we went fishing. To have said (rather than have written) "He and I, we went fishing," would be super-grammatically imperfect, surely?

(And you couldn't even say, "Him and me ..." without sounding pretensious, I trow.)