Chan went on to say Carey had been "trying to trademark this in every imaginable way" from music, clothing and alcohol, to "masks, dog collars - it's all over the map".
"If you knit a 'Queen of Christmas' sweater, you should be able to sell it on Etsy to somebody else so they can buy it for their grandma," she went on. "It's crazy - it would have that breadth of registration."
Carey's company did not respond to Chan's opposition in time so the trademark was not granted, meaning knitters around the world can continue without fear of breaching Christmas copyright.
The BBC has asked Carey's team for a comment.
Another singer, Darlene Love, previously took to Facebook to say she had been "Queen of Christmas" since before Carey rose to fame.
Love is known for her Christmas classic Christmas (Baby Please Come Home) and covers of hits such as Winter Wonderland and White Christmas.
Earlier this month, it transpired that Carey was no longer being sued for copyright infringement over her own Christmas hit, after country singer Andy Stone dropped his legal action.
The songwriter - who performs under the name Vince Vance with the band Vince Vance and the Valiants - sued the popstar in June, claiming he co-wrote a song with the same name five years earlier.
He told a court he would dismiss the case - but legally he could still refile it.
Christmas came early for Carey last week, when Netflix treated her to a special early screening of series five of The Crown at her home as a reward for being the show's "ultimate superfan".
