The story
From Shrek + -ing, referencing the animated fantasy film Shrek (2001), in which a princess falls in love with the titular ogre.
Etymology from Wiktionary, CC BY-SA 4.0.
Shrekking
Today it means: The practice of intentionally dating someone whom one finds unattractive, or less attractive than one desires, in the belief that this person will be more caring, faithful, or attentive as a partner. Full definition →