I see people discussing whether or not felons can be president. Tough call, but I can tell you as a naturalized citizen that's was adopted in 1970 at the age of 3, educated in the public school system, with nearly 22 years of distinguished military service, and no criminal record, I could never be president.
It was supremely irritating to be told all the time going up, "you can be anything you want to be," know full well that the rules clearly didn't extend that option to everyone.
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Only natural born citizens can be president. But you can hold any other office.
The qualifications for presidency do not address criminal records.
According to England, all the founding fathers were traitors.