Sounds like a great question for your doctor.

Not a doctor, but I can think of two possibilities:

1. Some vitamins and medications are water soluble, so taking them with water helps make sure it all gets into your system instead of being excreted.

2. 2L isn't very much for a full day. People are different, but even 2.5L/day is a little low for many healthy adults. This may be their way of getting you to make sure you're staying hydrated but framing it as a health necessity rather than just a recommendation. Even without the medication, 2L is probably a bare minimum for most people.

Could be that that medicine is (like coffee) a diuretic. They make you pee more so you have to drink more water to stay hydrated.

Im not a doctor. Adequate hydration (probably) increases flow, or your doctor thinks youre dehydrated, or the medication causes dehydration.

Doctor here. What medication is it? Why did they prescribe it? Do you have kidney problems?

As others have said, ask your doctor.

But to add another potential reason, some medications have dehydration as a side effect (maybe it messes with thirst cues, increases urination frequency, increases sweating, etc).

It might need to be fully dissolved in water to enter the bloodstream, otherwise it stays in the digestive track heading into the intestine and gets pooped out. But we're only able to guess if we don't know the medication.

Without knowing which medication, there can only be speculation as to why it requires a specific quantity of water. And even then, the best source of authority would be to ask the doctor for the reason.

I've found caffeine, and especially whatever they put in energy drinks, only interacts with my body in a helpful way when I'm not dehydrated. A Monster on a sweaty day does not get my ditches dug unless I'm chugging water too. Sorry I have no insight why, but maybe your med is a little like that.

Or perhaps it will cause the buildup of something toxic in your system if you aren't drinking enough water to flush it or its metabolic byproducts out.

Placebos? Docs trying to get you hydrated?