Because of the Nixon scandal and the break in that happened at the Watergate hotel
As far as I know that was the first use of the term gate, it was known as the watergate scandal
True story: when the Watergate scandal was TV news, I was such a tiny kid that I didn't get it and thought it was all about a dam. (A gate that holds back water.) I thought the president was somehow to blame for a burst dam somewhere.
Because Watergate, the name of the hotel where the Democratic party had their headquarters in the early 70s, was repeated so often in the news that it became a cliche while the Nixon administration was still being investigated. It was a part of American heritage while it was still unfolding. It came to be identified with almost any scandal.
Watergate is so well known.