Because of the milk.
When dining in Italy, there is no surer way to let the people around you know that you are a tourist than to order a cappuccino after your dinner. It breaks another of those Italian food rules that I often speak of: A cappuccino is for breakfast only.
First of all, most Europeans don’t drink milk the way that Americans do. An Italian adult drinking a glass of milk with dinner would be a rare sight. Italians are very conscious of digestion, and they know that milk during or after a meal can be hard on the body. (Their focus on digestion is the reason why there are so many wonderful Italian aperitifs and digestifs.)
Italians also don’t eat breakfast the way that Americans do. For most, a cappuccino and a small roll or pastry is breakfast. In fact, the only restaurants in Italy that serve an American-style breakfast are in hotels.
So, when a tourist orders a cappuccino after their dinner in Italy, they’ve essentially just ordered breakfast.