The idea that Shakespeare didn’t write Shakespeare arose in a nutty book around 1850 I think, and the arguments haven’t improved with age. :’)
There is no logic to the claim, no matter how “they” spin it. Some folks just aren’t happy until they become the epitome of stupidity.
I believe that it began with a descendent of one of the people suspected of being the “real” Shakespeare. And of course, for many people, it’s simply an intellectual snob’s argument. Shakespeare wasn’t educated well enough to be so talented, you see. Humph.