The constitution gives presidents broad powers to issue pardons for any federal (not state) crime. But allowing presidents to pardon themselves contradicts the whole thrust of the constitution, and the notion that people cannot be judges in their own case. The Justice Department Office of Legal Counsel has also opined that a self-pardon would be invalid.
The constitution’s framers feared unbridled power and sought to check the presidency in various ways. A self-pardon would sidestep those checks, creating a zone of impunity around presidents that would threaten democracy with autocracy.
Think of it. If presidents could self-pardon, they could rape, steal, or murder while in office and be immune from federal prosecution. They could commit treason, conspire with another country to get elected, or take bribes from foreign governments without fear of any criminal punishment.