And another one (Aruch HaShulchan if I recall): the special sacrifice on Shavuot were two loaves of bread. By eating two meals, one meat one dairy, you're forced to have two separate loaves of bread (total) for them.

I believe there's another one from the Zohar about how when blood runs through the mammary glands and is converted to milk, this represents the turning from G-d's wrath (blood) to mercy (milk), which happened as the Jews accepted the Torah. (This is also neat as the Talmud says the ratio of Divine strict justice to mercy is 1:500, ([based on Exodus 20:5-6][1]); well wouldn't you know it, but [according to this anatomy lecture][2], 

> On avg. 400 - 500 units of blood passes through the udder for each unit of milk synthesized by a high producing dairy cow


An interesting distinction among these answers is that according to some of them, you're just as well-off (maybe even better) eating only dairy on Shavuot (assuming ice cream makes you just as happy as steak); according to the first answer above, Alex's, and Monica/Aish #4, you should purposely have meat one meal too. 

  [1]: http://bible.ort.org/books/pentd2.asp?action=displayanchor&pentid=P2053
  [2]: http://classes.ansci.illinois.edu/ansc438/mamstructure/anatomy_7.html