Why can you eat meat after you drink milk, but not have milk after you ate meat for 6 hours?
Yes, it seems like a strange inconsistency. In fact, there are different customs regarding how long to wait. But the basic fact is that we wait after meat but not after MOST milk products.
The answer (and also why I wrote “most” above) has to do with physics. Meat takes longer to break down in the mouth and stomach than most milk products. Since the Torah prohibts eating milk and meat together, we wait longer after eating meat than milk. However, after consuming a milk product that breaks down slower, such as a hard cheese (perhaps parmesean would fit this category) the custom is to wait longer.
Moreover, even after drinking a glass of milk, we don’t immediately eat a hamburger, but first rinse the mouth (preferably with both a liquid and a solid such as a morsel of bread) and wash the hands, in order to keep the meat and milk totally separate.
Now in good Jewish fashion, I’ll end my response with a question for you. The Talmud declares that God didn’t want to deprive us, only to give us holiness and discipline, and therefore created a kosher way to get the taste of anything not kosher. Can you guess how one could get the taste of meat and milk together in a kosher way?