Why aren't we allowed to refreeze previously thawed breastmilk in refrigerator?
This is just a guess, but I don't think this is a food safety issues, its more a case of 'this food is gross now' issue.  

When I was a teenager I worked in a frozen food processing plant.  The freezers were giant boxes where freon was condensed on gigantic coils into a liquid and then the liquid freon would rain down on to the food passing under on a conveyer belt.  The vegetables were frozen instantly and it was quite tasty - frozen just a few minutes after being cleaned. 

As industrial freezing is very quick and such flash freezing, the quality of the food is preserved in a pretty fresh state. [its horrible for the ozone in the atmosphere but this was in the 80s and I hope they changed the process].  

Milk is a mixture of water based nutrients and globs of fat, which give the milk is homogeneous white color and its smooth texture.  Freezing milk in a typical refrigerator would take hours and ice crystals would form and separate out the two phases - the fatty portions would separate.  Try it with a glass of milk and see.   This is the same reason that you don't re-freeze ice cream, which has even heavier creme proportions (even fattier).  The texture is completely gone.