Let’s keep it simple.
Should you finish what you start? Yes.
If you’re braining yourself on a wall, should you continue? No.
Let’s say you’re me and you’re trying to stay on top of this whole writing thing while about a bazillion other things are going on. Dayjob, domicile maintenance, restocking pantries, getting fresh booze. If writing isn’t your primary vocation, you’ll have even less of this elusive thing called ‘free time’ from which to carve out the precious moments in which you make words appear from nothingness. You should spend it writing, not agonizing over whether or not you want to cause yourself pain through writing.
You see, you’re not always going to love what you write. In fact, there are times when you’re going to hate it. Maybe you’re just sick of a work in general, or perhaps you’re kicking yourself in the gonads for a particular aspect of it. The opening may slog, the characters may feel uninteresting, there’s no tension, the action has no bite to it, so on and so forth. Whatever the reason, opening that file or notebook now fills you with a profound sense of dread and/or nausea.
Yes, writing is work and work means not always doing what you want but rather what you must. But be honest with yourself. It may be time to put your project aside and strike up another. There may be a fundamental flaw that, given your proximity to the work, you’re simply not seeing.
The important thing is that you don’t stop writing. And while scribbling on cocktail napkins or rambling in a blog is all well & good, you need to keep up with your primary area of focus, be it speculative fiction or mouth-watering recipes. Write what you want when you can, and just like you shouldn’t be afraid to try something new, you also shouldn’t be afraid to put something aside that just isn’t working. You can always come back to it later. And who knows? Maybe those old ideas can be pulled into something new, provided they don’t turn into a lead weight that drags the whole thing down into the depths of the Stygian pit.
More on that later.