This isn't true. They don't have to like find a statute to impeach him under. They can just make up reasons. There aren't really any Supreme Court cases that limit impeachment power. "High crimes and misdemeanors", in its original usage basically just means "for whatever reason deemed appropriate" and covers "crimes" that aren't necessarily written down, like being dangerous to the state, appointing idiots, not doing your job, conduct unbecoming of the position, or violating your oath of office.
Most of these are not probably crimes, as in there is nothing written down anywhere for the FBI to investigate "being a shitty president".