The following Presidents of the United States graduated from Harvard ( only Bush Jr. had an MBA ) :
* John Adams
* John Quincy Adams
* Rutherford Hayes
* Theodore Roosevelt
* FDR
* JFK
* Dubya
He later wrote that he got most of his valuable real world education as a young rancher in North Dakota. So I think you should forgive him for the Harvard degree.
Also, you left BO off your list.
Hayes and Teddy Roosevelt were also military officers.
So, I’ll see your list of Harvard grads and raise you a list of Presidents with military service:
Washington
Jefferson
Madison
Monroe
Jackson
Harrison
Tyler
Taylor
Fillmore
Pierce
Grant
Hayes
Garfield
Arthur
Need I go on?