Then, the whole process of how they make milk 'skim' is not pleasant. Basically, the fat free milk is fortified with dry milk to increase the protein content (add back what has been taken away). That dried milk is made at high temperatures which damages the nutrients. Vitamin A must be added back, because any natural form of it was also taken away during the de-fatting process (A is a fat soluble vitamin). If it is not synthetically fortified, any Vitamin A needed to process the added proteins is taken from the liver; could lead to depletion over time if you do not get enough Vitamin A from other sources.
A sneaky side of the whole fat-free dairy issue is that the cream/fat that is extracted is then used in other products. Gives more profit from the same quantity of milk to the company at the expense of giving you a lower quality yogurt.
Are you eating this to reduce your calorie intake? Fat in your diet will actually curb your appetite and lead to a lower calorie intake overall *without* the horrible feeling of deprivation and hunger! Fat is needed for you to utilize the protein in dairy so fat-free dairy isn't as nutritious as you'd hope because you might not be getting a lot of the nutrients.
if you are looking for some quality food to put into your body that isn't freaking you out with calories, then go for full-fat, plain yogurt. It is GOOD. Greek yogurt is decadent. Not a whole lot of calories that tastes so good going down.