Phrases – Does the ‘Crux of the Matter’ Phrase Make Sense?

It is an easy logical step from first off to second off, and there’s no grammatical argument against it.

However it is exceedingly rare, and markedly informal, if the Corpus of Contemporary American English is any indication. I found only three uses:

There about a thousand things wrong with what I’m hearing him tell me to do. First off, if you burn the money they can’t have it cause it’s all burnt up. Second off, Heaven don’t have a checking account at the Bank of Hell.

“First off,” Amanda said, “I ain’t movin shit. Second off, it ain’t no thing. It’s a classic. Third off, you better get out my damn face. This a free country, man. You ain’t no fuckin parkin police.”

First off, who’s your inspiration? Second off, is there any truth to the rumor between you and Justin?

Note that the first two are from fiction, and both those characters are using a decidedly non-standard dialect. So only the last item is something someone just naturally said. That’s just one use of second off in a 425 million word corpus.

Anything that rare is going to sound funny to people, so I recommend avoiding second off.

What you're observing is a phenonmenon called lexicalization. Consider the following sentence:

What is the matter?

Here the speaker assumes that some problem exists and asks what that problem is. "The matter" means "the matter of concern"; i.e., the thing that we should be worried about. This makes perfect sense on every level of analysis.

But through the repeated use of this expression or some similar one, the phrase "the matter" has become lexicalized into an expression of its own, carrying the sense of "something that we should be worried about". The word "the" here cannot be analyzed on its own. That would be like if you said that you were going to say something, and I asked you where you were going. Here the word "going" is relieved of its usual semantic duties in order to work a side gig as part of a lexicalized aspect marker.

Is this lexicalized usage of "the matter" logical? Not especially, but langauge doesn't need to be logical—not even formal, educated, standard language. If it intelligibly communicates its intended meaning, then, by definition, it makes sense.