“Do I look like a biscuit to you? Do I look like a fucking French fry? Then why are you trying to play me like a side order?” -- from the romantic comedy film, Hav Plenty (1997)
Let’s put the term in its proper context. A man orders a meal from Whataburger: a cheeseburger, large fries, and a large drink. He only barely manages to finish it and finds himself extremely satiated. A few days later he returns and orders the same thing and consumes it on location. In the midst of eating he realizes he’s hungrier this day than he was the other day; he’s going to need a side order of something-- extra fries, tator tots, a salad, apple pie, chocolate malt, etc.
A man can be satisfied by a woman for a time but then suddenly feel the need for a side order. This could be a one-night stand or a longer affair-- whatever he needs to be satiated. This says nothing about the abstract quality of his regular "meal"; he simply desires something extra, or something new.