Why do we use the suffix “‑gate” when referring to a scandal? [closed]

This is a great example of a back-formation: a word is treated as if it were composed of prefixes or suffixes, then taken apart (incorrectly) and remixed to form new words. Another famous example is cheeseburger. The ‑burger suffix is incorrectly taken from hamburger, which is a dish from Hamburg, not a burger made from ham.

Watergate was a big enough scandal, and sounds enough like it’s composed of Water‑ and ‑gate, that the suffix has been back-formed into plenty of other scandal names.

Watergate was the name of the office in Washington where the scandal broke out. Hence the original 'gate' form - Watergate. Thereafter, any sort of scandal is given the 'gate' suffix as a sort of derivation of Watergate. This is true even for media coverage of smaller scale controversial events. In cricket, a couple of years ago, one cricketer slapped another cricketer who was heckling him. The incident was publicised as Slapgate. It's that easily used.

This sort of referencing also finds its way into the film industry - As a tribute to Hollywood, we have Nollywood in Nigeria, Bollywood, Kollywood and Tollywood (2 of them!) in India, Lollywood in Pakistan.

This sort of derivation is attractive when the original word has multiple syllables and a recognisable morpheme (like wood, gate). One can imagine that Woodstock could have given rise to a whole group of festivals with 'stock' as the keyword.

As for the process, refer to this: Pormanteau. It's another method of neologisms.