We may never have a definitive answer, but it is very difficult to reconcile the humble circumstances of one William Shakspere (sic) of Avon, with the encyclopedic knowledge and vast experience required to write those plays.
I’m not sure what “humble” implies, but his mother was from a wealthy family and his father was alderman and mayor. (Not that being rich makes you a better writer, but it explains how he could get this education.)
And “vast encyclopedic knowledge” is overtating it somewhat. His plays are fiction and use a lot of artistic license, like placing the royal court of Denmark in Elsinore.
It also bothered them that Shakespeare was an actor, since actors at the time was considered lower status. So by separating the actor Shakespeare from a hypothetical aristocratic author, the prestige of the greatest author of the English language was saved.
It was also rather embarrassing that Shakespeare was part owner of the Globe Theater and seemed to have been a savvy businessman, becoming wealthy through his career. This was embarrassing because a proper aristocrat and poet should of course be elevated above any concerns about earning money (as opposed to just naturally having them).
Try Charles Nicholl's The Lodger for a pretty detailed study that leaves little room for doubt about the fellow from Stratford.
The anti-Stratfordians have absolutely no evidence other than speculation and snobbery.
Eh. In practice, if in doubt, he made it up, particularly in respect to geography. If anything this is an argument against the “Shakespeare must actually have been aristocratic” thing, if anyone still took that seriously.