Here is an explanation of Shakespeare's argument:
Time's Effects on Summer: Shakespeare begins the sonnet by comparing the object of his affection to a summer day, highlighting the beauty and pleasantness of such a day. However, he then acknowledges that summer days are fleeting and subject to change. The summer's breath, or wind, can be too harsh or too mild, and the sun, which makes the day beautiful, can also be scorching or hidden by clouds.
Unchanging and Perfect Beauty: In contrast to the changing nature of summer, Shakespeare asserts that the beauty of the person he is addressing is unchanging and everlasting. He says, "But thy eternal summer shall not fade, nor lose possession of that fair thou ow'st." This means that the person's beauty will not diminish over time, nor will it be affected by the harsh realities of the world.
Immortalization Through Poetry: Shakespeare suggests that the person's beauty will be made immortal through his poetry. He says, "So long as men can breathe or eyes can see, so long lives this, and this gives life to thee." By writing a poem about the person's beauty, Shakespeare ensures that their memory and beauty will live on even after their physical existence ends. His poetry becomes a testament to their everlasting loveliness.
In essence, Shakespeare's argument is that the beauty and worth of the person he is addressing transcend the limitations of time and the natural world. By immortalizing their beauty in his poetry, he ensures that they will be remembered and admired for generations to come.