Shakespeare hands a young man a mirror and tells him to have children
Sonnet 3 opens with a command: look in the glass. The face staring back, the speaker argues, owes the world a copy. Refuse to father one and you cheat some woman of motherhood, bury your own posterity, and let your image vanish when you do. Vanity becomes a duty to reproduce.
The poem is built around mirrors. First comes the literal looking glass, in which the young man is told to study his face and see that the moment has arrived for it to make another. Then the image doubles back: he is himself his mother's glass, and when she looks at him she recovers what the poem calls the lovely April of her prime. Finally the speaker projects forward, promising that a child will one day be a window through which the ageing man can glimpse his own golden years, wrinkles notwithstanding.
Between those mirrors sit two blunt rhetorical questions. What woman is so beautiful that she would scorn his farming of her unploughed womb? And what man is so foolish that his self-love would make him the tomb of his own line? The agricultural language of tillage and husbandry turns courtship into cultivation, and the word husbandry carries a pun on becoming a husband.
The couplet lands the threat without softening it: "But if thou live, remember'd not to be, / Die single and thine image dies with thee." Here remembrance depends entirely on offspring. A bachelor who wishes to be forgotten, the speaker implies, is free to stay single, and oblivion will be the price.
The maternal mirror has a biographical echo. Shakespeare's own mother was Mary Arden, the daughter of an affluent landowning family influential among Warwickshire's recusant Catholics, while his father John was a glove-maker and alderman who had come from Snitterfield. William, baptised in Stratford-upon-Avon on 26 April 1564, was the third of their eight children and the eldest son to survive.
Source: Sonnet 3: Look in thy glass and tell the face thou viewest