Just going to post the math.
You start with 6 ounces in each glass. You move one ounce of red into the white.
The white glass now has 6 ounces white and 1 ounce red. The red glass has 5 ounces red.
Then you move one ounce back. This one ounce contains 1/7 ounce red and 6/7 ounce white. (the proportions that are in the white glass)
So, subtracting this from the white glass we have 6/7 ounce red and 5 1/7 ounce white.
Adding to the red glass we have 5 1/7 ounce red and 6/7 ounce white.
They are both contaminated by the same amount! It's unintuitive until you actually do the math :)