There were two parties to the Civil War. The fact that each of those parties was made up of smaller individual parts is immaterial to Brutus216’s original analogy. But if it makes you feel better, the Northern States versus the Southern States was absolutely already a thing going back to the constitutional convention.
The body analogy, however, does break down very quickly. If the body separates, both parts will die. If the country separates, both parts will simply become their own country. Will they be weaker? Sure. Would they have been smarter to work out their differences and stay together? Absolutely. But neither side will immediately perish because of the exit of the other.
I understand the desire to employ something like the body analogy, especially in light of Lincoln’s famous “house divided against itself” argument. The fact is, it’s the body analogy, and not the marriage analogy, that breaks down. It’s the equivalent of the husband saying, “But I’ll die without you! You’ll die without me!” right before he starts beating the wife in the marriage analogy.
Incidentally, the body analogy has a long tradition in the history of people in power trying to keep other people in line. Google “the secession of the plebs” in Roman history to learn about its earliest recorded use.