The authorship of the plays is really a nonquestion, interesting to people who think that Dan Brown fellow was writing about real history with all that code and secret society stuff. It didn't occur to anyone to question the authorship of Shakespeare's plays until more than two hundred years after his death and doing so makes about as much sense as questioning that Dante or Dickens or Poe or Atwood wrote the works we put their names on; once someone asks the question, though, the anomaly hunting and convoluted storytelling begin and you can find reasons to question the truth of just about anything if you want to badly enough (moon landings, anyone?). The refusal to believe Shakespeare wrote his plays depends on a few basic ideas and ways of thinking.
First, a highly Romantic idea of authorship, with the Artist an exalted figure, someone touched by a kind of mysterious spiritual power we call Genius, set apart from the ordinary, working in isolation, against the grain of his/her (usually his) society, a rebel, a prophet, producing Art for a tiny elite of people sensitive enough to hear the Truth (if not sensitive enough to produce Art themselves), rejected and unheard by the masses who can't bear to face the Truth of Art. This is a conception of the Artist and of Art that would have made no sense to anyone before the Romantics came up with it in the late eighteenth and early nineteenth centuries (which is why it occurred to no one to think of Shakespeare in this way until then). But it is utterly incompatible with any evidence that the Artist, especially the great Shakespeare, operated in the real world of practicality and business and money and family and property and contracts and debts and legal documents and co-workers; such things are far too mundane to associate with Art. And so the mundane Shakespeare, who sued for the repayment of debts and expected to be paid for his work and bought property and wrote a will some people now don't approve of and worked with other people, couldn't be an Artist.
Second, basic snobbery. Great Art is produced by sensitive, highly educated, well-traveled, privileged, sophisticated people with sensibilities far above those of ordinary people who work for a living and come from small towns and wear boring clothes and worry about the rent. You know, like aristocrats and people who associate with aristocrats. Because aristocrats are so much more sensitive and exciting and glamorous than boring ordinary, nonaristocratic people. So boring, ordinary Shakespeare from a boring, provincial town, who associated with other boring, ordinary people (and even married one), and didn't travel and didn't grow up with all the privileges and wasn't educated at an elite school couldn't possibly have produced these plays about sophisticated, complicated, interesting people, because he was ordinary in his background and connections and ordinary people aren't capable of imagining things they haven't personally experienced.
Third, a fascination with conspiracy and a pride in being one of the few who are in on the secret. The world we see is dull, but underneath the surface, it is full of intrigue and mystery and scheming and plot-making, except that most people are too lazy and pedestrian to see it properly. So it falls to the few who are able to see beneath the surface to expose the conspiracies that lurk in the shadows. We should be grateful to them, really, but they, like Artists, are usually unappreciated and unrecognised by the masses as the visionaries they are.
Fourth, the autobiographical fallacy, the idea that authors are really always writing about themselves, that they can only write about they know and have experienced themselves, that they are prisoners of their personal psychological makeup and constantly revealing it even (or especially) when they think they are writing about someone else who isn't them, that fictional characters are always alter egos for their authors (except when they aren't) or portraits of real individual people who can be identified by name. And lyric poetry above all, like the sonnets, is explicitly and narrowly autobiographical and can't possibly be anything else and the "I" of a poem is always the author.
James Shapiro is remarkably patient with all this stuff, and you could not ask for a more helpful guide through the labyrinth of the authorship question (or nonquestion). He lays out clearly the roots of the problem, the motivations for questioning Shakespeare's authorship (and the history of the issue and their reasons for asking the question are far more interesting than their convoluted answers). As he points out, there is a great deal of evidence that his contemporaries knew Shakespeare as an author, as the author of his plays, and none whatsoever that he wasn't. And if you start thinking about the practicalities of the conspiracy it would have taken to hide the authorship of someone else under his name (let alone why it would have occurred to anyone to have done such a strange and difficult thing, especially at a time when anonymous publication was so common and so easy), just who would have had to know enough to be dangerous, how many people had to keep how many secrets, you realize what nonsense the whole thing is. People just aren't that good at keeping secrets, at being consistently competent and controlled enough to make a conspiracy of this magnitude work. This is where conspiracy theories always fall down: I just don't believe in cabals of master-plotters who never slip up, never make a mistake, and who are perfectly in control of secret information.
In some ways, of course, the identity of the author doesn't matter. The play's the thing, after all. But Shapiro has a thoughtful response to the temptation to dismiss the whole matter (as most academics have done): "When I first explored the idea of writing this book some years ago, a friend unnerved me by asking, 'What difference does it make who wrote the plays?' The reflexive answer I offered in response is now much clearer to me: 'A lot.' It makes a difference as to how we imagine the world in which Shakespeare lived and wrote. It makes an even greater difference as to how we understand how much has changed from early modern to modern times. But the greatest difference of all concerns how we read the plays. We can believe that Shakespeare himself thought that plays could give to 'airy nothing' a 'local habitation and a name.' Or we can conclude that this 'airy nothing' turns out to be a disguised something that needs to be decoded, and that Shakespeare couldn't imagine 'the form of things unknown' without having experienced it firsthand. It's a stark and consequential choice."