I said I had an even better solution but @byorgey beat me to it and @zzq then nailed it as well. For completeness though, here’s my own explanation, inspired by how I convinced @faire (age 11):
If you think about how a teaspoonful of wine leaves the wine glass and the water gets slightly contaminated and then some but not (necessarily) all of the wine comes back to the wine glass it’s all very confusing. The trick is…
…to ignore all the back-and-forth and think only about how the glasses start and how they end up. You start with exactly a glass full of wine and you end with a glass full of mostly wine. But the glass is still exactly full at the end – a teaspoonful of something left and a teaspoonful of something came back.
So some fraction of a teaspoonful of wine got displaced by water and there’s only one place it could go: the water glass! That fraction of a teaspoonful could even be the fraction 0% or 100%. Say you move a teaspoonful of wine and it sinks to the bottom of the water (why not?) and you move only water back. Then you have 1 teaspoonful of wine in the water and 1 teaspoonful of water in the wine. At the other extreme, if you dump the teaspoonful of wine in and manage to scoop exactly that wine right back out then you have 0 teaspoonfuls of wine in the water and 0 of water in the wine.
For anything in between it’s the same story: Since the wine/water levels in the glasses end up the same, however much net wine  left the wine glass is exactly how much water must’ve replaced it.
 Keeping this 11-year-old friendly, the amount of net wine that leaves the glass is the amount that left minus the amount that came back. So like the amount that really actually left, not just the amount that initially left. Like how net profit, for example, is the amount of money you really actually made, subtracting all the money you spent as part of making it. The final amount in your pocket. Or the water glass, in this case.