Generally, it’s a good rule of thumb to avoid calling the speaker of a poem by the name of the author. The idea is that the speaker in a work of literature, describing the subject matter, could very well be (and often is) another kind of character created by the author.
But Shakespeare makes things tricky: what if that speaker acknowledges that he’s writing a poem? Doesn’t that mean he is Shakespeare, the writer of this poem? Well, this certainly makes the speaker look a lot more like the Bard, since this is a poem in a book of poems by William Shakespeare. Still, we have to keep in mind that they’re not necessarily the same, since we can easily imagine Shakespeare inventing a character who writes poems. For that reason, we’ll keep calling him the speaker instead of Shakespeare.
Now, this speaker is one cocky son of a gun. You can tell that he’s the kind of guy who says annoying things out loud to pump himself up, like, "You’re damn right you look good in this new blazer" while posing in front of a mirror. The fun for him is seeing how great he is.
The poem is an ego trip from start to finish. That rhetorical question to open things up? It’s just that: rhetorical. He knows we’re not about to say, "No, you shan’t compare anyone to a summer’s day." If he said, "Shall I go abuse my adorable puppy?" we’d have no way of stopping him. He’s got us right where he wants us, and by asking a question we can’t possibly answer, he’s already on a power trip, since we’re not about to quit reading this little 14-line poem.
In the second line he makes his one and only concession to "thee," recognizing that he or she is "lovely" and "temperate," but check out the stresses in these first two lines: "I" is a stressed syllable but "thee" and "thou" aren’t! And from then on it’s even more brazen self-congratulation. He goes into a bit of indulgent, very poetry-ish personification of summer and nature, and then swoops in for his grand entrance as God, announcing: "Behold my power, for I have made you, unlike summer, immortal."
And here’s what makes it extra irritating: he’s right. He thinks he’s a stud and he’s spot on – if you’re reading the poem (which you just did), he’s given "thee" new life, or at least "life" as he defines it, which is being analyzed and admired. But give that a second thought: has he really given the beloved something summer doesn’t have? Isn’t he tooting his own horn a bit? The summer is discussed and admired eternally, since it comes around every year, and so isn’t all that different than the beloved as presented in the poem. You could, then, see the speaker as a delusional self-flatterer, strutting his stuff on the stage.