“How sharper than a serpent’s tooth it is to have a thankless child!”
The image captures the particular hurt of care being answered by ingratitude within a close family bond.
Source details
King Lear, Act I, Scene IV, reviewed against the scan-backed First Folio facsimile. Lear's serpent's-tooth line occurs inside his curse against Goneril after the reduction of his retinue; it is angry dramatic speech, not a neutral rule about children or family relationships.