From the article:
But according to Politico, it wasn’t the gum chewing that displeased Trump. “More than being lampooned as a press secretary who makes up facts,” a source close to Trump told the Web site, “it was Spicer’s portrayal by a woman that was most problematic in the president’s eyes.”
Yeah, when I saw the segment, my thought was that this is the beginning of the end for Spicer - dt won't be able to stand having someone as press secretary whom he views as having been emasculated.