The ANSI SQL standard format for date is YYYY-MM-DD HH:MM:SS. It's easier to capture the date in this format for insertion into a database.
In order to store the date with the format you're using (MM-DD-YYYY) you need to use the STR_TO_DATE function which allows you to convert a string to a date. The syntax for this function is:
STR_TO_DATE(str, format)
The specifiers for the format can be found here.
For your INSERT statement, you would use:
INSERT INTO `user` (`dob`) VALUES ( STR_TO_DATE('13-07-1990','%d-%m-%Y') )