And another one (Aruch HaShulchan if I recallRama OC 494): 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); well wouldn't you know it, but according to this anatomy lecture,
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.