I wrote an answer to this on another question.
Because they wanted and still want to be different. It is quite illogical to write it this way. YY/MM/DD would have been more logical. It the military they use DD/MM/YY format.
On immigration forms also they use DD/MM/YY format.
Another fun fact: 110V is also only used to be different. The power coming to all homes in US is 220V, but they divide it by 2 to get 110V. Just to be different.
Brijesh Kumar's answer to Why does USA use MM/DD/YY as date pattern contrary to the rest of the world?