I have been told that the Irish don't celebrate St. Patrick's day like the US does. They celebrate it, but it is just not that big of a day for them. It is a quieter celebration. I learned today that Cinco De Mayo isn't even celebrated in Mexico.
On May 5th, 1862, France attacked the Mexican city of Pueblo. Mexico owed France, England and Spain a lot of money but France is the only one that didn't come up with a peaceful resolution to the problem. Mexico's victory on this day became a symbol of Mexican unity. A year later, the people of California (that seceded from Mexico sixteen years earlier) celebrated Cinco De Mayo to to acknowledge Mexican independence. The tradition spread throughout the states.
September 16th, the day that they declared indepedence from Spain in 1810, is the Mexican Independence Day that is celebrated today.
Check out this excellent aritcle from the Huffington Post: Huffington Post link