He was impeached because the GOP wanted to impeach him, no other reason necessary. The investigation started as a look into the Clintons' finances before pivoting to the affair after their operatives caught wind of it. Even the charge of lying to Congress (which failed because he'd asked them to define sexual relations and used that definition when stating he hadn't) was a last-ditch attempt to get him on anything they could after repeatedly failing for years.

They later repeated the tactic with the Benghazi/private email server "scandals" to discredit Hillary Clinton.