No, it doesn't.

of course it does. pasteurization involves rapidly heating and cooling the milk to kill off bacteria and viruses. Thats going to denature a lot of enzymes as well as change the structure of a lot of proteins. To say that no vitamins or nutrition is affected is an incredulously false to make here

I think the parent meant

"`for any choice of (∀) nutrient, pasteurization kills nutrient` evaluates to false"

Rather than

"`any nutrient (∃), pasteurization kills nutrient` evaluates to false" - which is what you seem to be responding to.

A study back in 1974 reported that vit. D in milk was unaffected by pasteurization, boiling, or sterilization.

Hartman, A. M., and L. P. Dryden. 1974. Vitamins in milk and milk products. Pages 325–401 in Fundamentals of Dairy Chemistry. 2nd ed. B. H. Webb, A. H. Johnson, and J. A. Alford, ed. AVI/ Van Nostrand Reinhold, New York, NY.

Different cooking methods for other foods can alter the D content but not drastically it seems. (https://pubmed.ncbi.nlm.nih.gov/29548435/)

How would this affect the added vitamin and fat?

It helps the poster build a straw man argument.

The effect of cooking on nutrients varies widely, depending on the specific cooking process and the nutrient in question.

"Nutrients" are typically defined as proteins, carbohydrates, lipids (fats), vitamins, and minerals.

Vitamin C is not very heat-stable, so you generally need to get that from raw fruits and vegetables (unless the food has been supplemented with it after cooking).

Vitamin D, by contrast, is pretty heat-stable.

Some proteins are rendered much more digestible by heat, so cooking actually improves the nutritional value of the food, in some cases by a great deal.

Lipids aren't generally affected much, though again some are more heat-stable than others. This is why some fats and oils are a better choice for deep-frying.

Carbohydrates are generally rendered more digestible by cooking, if anything (as long as they don't get so hot they start burning).

Minerals are mostly unaffected by heat. They can leach into the cooking water, so you'll lose some minerals if the cooking water is discarded. If it's something like soup, where the liquid is consumed, there's little or no impact.

There are even some commonly-consumed foods that are actually toxic unless they are cooked or otherwise processed. Cassava and some types of beans fall into this category.

I don't want to make a blanket statement, but I'd reckon that overall cooking helps more than it harms. Note that cooking is nearly universal across human cultures. Some cultures eat a lot more raw foods than others, true, but even the most raw-loving groups generally have some foods they cook (or otherwise process to break down, for instance, by fermentation).