The story
From queer (“transgress or reevaluate, especially in accordance with queer theory”) + platonic (“non-sexual and non-romantic”). Coined by Dreamwidth user Meloukhia in 2010 who further popularized it in 2011 through posts on WordPress and Tumblr and said it "describ[ed] relationships where an intense emotional connection transcend[s] what people usually think of as ‘friendship’ is present, but the relationship is not romantic in nature […] though [it] can be sexual".
Etymology from Wiktionary, CC BY-SA 4.0.