Can I use the verb "finish 'in present continuous tense?

Recently, in an essay, I used "finishing up" in a sentence. My teacher marked it wrong, because to finish something isn't an action that takes time. But I've heard "finishing up" used in real life. Is it grammatically correct to use finish in present continuous tense?

Solution 1:

Any action, including finishing something, takes a measurable amount of time between its start and its completion. It's not possible for any action to occur instantaneously, even if its length of time isn't perceptible. There will always be some moment before and some moment after—and some amount of time in between those two moments.

Further, if you're able to say that you're finishing up, then what you're doing is taking a perceptible amount of time—at least as long as it takes to say that, but most likely longer.

Your teacher may have been confusing finishing up with something like this:

I am finished.

That doesn't involve time, because finished in that sentence is an adjective, not a verb, and it's describing a property or attribute.