It is there in black and white
So far, no authorship theory has presented stronger evidence than the name written on the works in black and white.
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We know that a man named Shakespeare wrote the plays. He put his name on them.
Contemporary documents show that this man was named William Shakespeare. He was the son of a glover and educated at Stratford Grammar School in the town of Stratford-Upon-Avon. We know he married Anne Hathaway. We know he was an actor and we know he died in 1616. This is what the documents say and there is no convincing evidence to the contrary to suggest he did not write the plays.
All that tells us is that there was a man from Stratford called "Shaksper" and that, for whatever reason, the similar name, "Shakespeare" or "Shake-Speare" appeared on a number of plays attributed to him. That does not prove that he wrote them. Books were often printed without an author and often under pseudonyms.  We don’t even know if that is how he spelt his name. The only surviving example of Shakespeare’s writing are six scratchy signatures spelt several different ways. There is also significant evidence to suggest he did not write the plays. What we know of his education suggests that the Stratford man may not have had the necessary schooling to produce works of the calibre attributed to his name, because there is no documentation for his having attended school in Stratford, only assumption.
[P1] Shakespeare's name is on the plays in black and white. [P2] There is no compelling evidence to the contrary to suggest he did not write the plays. [P3] Therefore, the logical conclusion is that Shakespeare wrote the plays.
Rejecting the premises
[Rejecting P3] There is significant evidence to suggest that Shakespeare did not possess the necessary education to write the plays and sonnets.