Shakespeare begins "Sonnet 18" with a question because his speaker is struggling to determine how to begin a poem praising his beloved. The easy and conventional way to address her would be to compare her to a summer's day. He has seemingly read many sonnets that begin this way.

Shakespeare, who liked to turn conventions on their heads, decides not to do this. Instead of having his speaker liken his beloved to the perfections of summer, he dwells on the ways summer is imperfect or inconstant: it is too short, sometimes it is too hot, and sometimes it is cloudy or windy. In contrast, what makes his beloved beautiful never changes. He states that her

eternal summer shall not fade

This implies that what he loves in her is her unchanging soul, not her external qualities, a point he will make in other sonnets.

By beginning with a question, the speaker is giving a species of soliloquy. In drama, a soliloquy is a way for an actor to express his inner thoughts to an audience. Here, the speaker is thinking aloud, musing about his beloved as he begins his poem. He is able to think past the limiting conventions and artificialities of the poetic form to convey what his beloved is really like to him.

In Mrs. Shakespeare's Diary, Robert Nye includes the following pithy exchange:

"Shall I compare thee to a summer's day?"
"No thanks."

In fact, Shakespeare did not ask this question to Anne Hathaway, or even to the Fair Youth of the sonnets, but to himself. The rhetorical strategy gives the sense of eavesdropping on Shakespeare's creative process, as he works out the grounds for comparison and resolves each of them in favor of the addressee.

The most famous sonnet in the English language is a victim of its own success. Everyone knows the end, so no one is surprised by it. However, if you were approaching the sonnet for the first time, you might guess at a rather different final couplet, particularly if you were familiar with Renaissance verse. The summer's day is beautiful, yet transient. These are the grounds for comparison.

The beloved is even more beautiful than a summer's day but, as a poem in the Horatian "carpe diem" tradition might insist, almost as transient. Your youth and beauty will not last long, so let us love each other now. This is the message of Marvell's "To His Coy Mistress" and many other love poems. Instead, Shakespeare steps in with his own poetic genius as the unexpected answer to a conventional question. The beloved addressed is not as transient as a summer's day. Thanks to Shakespeare, s/he is immortal.

Why does Shakespeare begin Sonnet 18 with a question?

Sonnet 18 begins with one of the most famous opening lines in all of Shakespeare’s sonnets: “Shall I compare thee to a summer’s day?” In literary terms, this is a device known as a rhetorical question, since the author is not actually expecting an answer. It is an effect to make the language more poetical, as well as to move on to the next thought. By framing the opening line as a question, Shakespeare also sets up a dynamic between the author and the subject. It can allow the reader to feel as if they are the subject (the “thee” in this case referring to the reader) which makes the rest of the sonnet more tender and personal. It frames the author as a lover, idling away his time with rhetorical questions. It also allows the author to address the subject of the sonnet directly, which gives it the mood of being a true love letter sent from one person to another. Lastly, the question at the beginning of the sonnet gives the sense that Shakespeare is coming up with the sonnet on the fly, as if the words are tumbling out of him and he has never thought to compare his subject to a summer’s day before.