Why did Sarai want to send Hagar away?
Sarai wanted Hagar sent away because Hagar, after conceiving, became arrogant and puffed up, despising Sarai and making life nearly impossible. Sarai felt wronged and asked Abram to send the young woman away; when she dealt harshly with her, Hagar fled.
Les explains that Sarah, impatient about having a son, proposed that Abram go into her maid so she might obtain children by her. After Hagar conceived, she saw she had one up on her mistress Sarai and became arrogant, puffed up, and almost impossible to live with. Sarai then begged Abram to send the young lady away, saying she was despised in Hagar's eyes. Abram put Hagar in Sarai's hand, and when Sarai dealt hardly with her, Hagar fled.
And he went in unto Hagar, and she conceived: and when she saw that she had conceived, her mistress was despised in her eyes.