The Gemara in Bechoros 6b searches for a source that one is allowed to consume milk. There are several possibilities of why it may have been forbidden, which we will explore. The Gemara cites the pasuk of Eretz zavas chalav u’devash – a land of flowing milk and honey, and explains that the Torah would not praise Eretz Yisrael with something that was forbidden.
However, the Shita Mekubetzes there asks why the Gemara did not cite the pasuk in this week’s parshah where Avraham Avinu served his guests milk. Surely Avraham Avinu wouldn’t serve something forbidden. The Shita Mekubetzes answers that the reason that the Gemara thought that milk would be forbidden was because it was basar min hachai – literally meat from a live animal. This differs from eiver min hachai, which is specifically a limb from a live animal. Anything that is not a limb that comes off an animal is considered basar min hachai. The Shita then explains that bnei Noach are allowed to eat basar min hachai, they are only prohibited from eating eiver min hachai. Since Avraham thought that his guests were bnei Noach, he served them milk, and we can draw no proof for our usage of milk.
However, not all Rishonim agree that bnei Noach are allowed to eat basar min hachai, the Rambam (Hilchos Melachim 9:10) explicitly writes that they are prohibited from eating basar min hachai as well as eiver min hachai. So, the answer of the Shita will not work for the Rambam.
The Noda Beyehuda (Tinyanah Yorah Deah 36) explains that the reason that milk would have been forbidden was not because of basar min hachai or eiver min hachai. This is because milk is not an eiver (limb) or bassar (flesh). Rather the potential problem that milk could have is that it comes from an unshechted animal. Anything that comes form an unshechted animal is prohibited because it did not yet have shechita. However, bnei Noach who may eat an animal that was not shechted, would have no issue eating milk. Therefore, the Gemara could not have cited the pasuk where Avraham served his bnei Noach guests milk as a proof that we may consume milk.
Rav Akiva Eiger in Chullin 98b explains that the potential prohibition that milk would have is that it comes from a forbidden animal; a live animal. Every live animal is forbidden to eat, while it is alive. The halachah is that anything that comes from a forbidden animal is itself forbidden. For example, if a non-kosher animal gives birth to a kosher animal that has the kosher signs, it is nevertheless forbidden since it came from a forbidden item. It is this prohibition that we would have associated with milk if not for the pasuk that the Gemara cites.
Based on this explanation we can suggest another answer to the Shita Mekubetzes’s question. Bnei Noach are not prohibited to eat something that comes from a forbidden animal. Since Avraham assumed that his guests were bnei Noach, the Gemara could not cite the pasuk whereby Avraham served milk to his guests to prove that we may consume milk.
Some Rishonim are bothered by the opinion of the Rambam that bnei Noach are commanded not to eat basar min hachai. After all, the source for this prohibition in the Torah is a pasuk in Parshas Mishpatim: basar basadeh traifa. The Gemara in Chullin 102b derives from here that basar min hachai has the status of traif. Bnei Noach are allowed to eat traif meat. Why then would they not be allowed to eat basar min hachai?