Why did Abraham have a child with Hagar?
Abraham had a child with Hagar because he and Sarah remained childless, grew impatient, and Sarah suggested the custom of using her slave girl to produce an heir. Abraham, equally eager for a son, agreed, taking God's delayed promise into their own hands.
Les explains that Abraham and Sarai had no son, so being human they got impatient. Sarah suggested, according to their custom, that Abraham have a child by their slave girl Hagar. Abraham, just as anxious to have a child, immediately agreed, and Ishmael was born. But Ishmael was not the son of promise; he was after the flesh, while Isaac was the son of promise. Les points out that many years passed—25 before Abraham left Haran, then another 14—until they finally decided God was not going to do anything and took it into their own hands. Abraham was 86 when Ishmael was born; God's promised son did not come until he was 100, after a 50-year wait.