Why did Rebekah’s father want to wait 10 days before he sent her with Abrahams servant?
Genesis 24:54,55 And he and the men who were with him ate and drank and stayed all night. Then they arose in the morning, and he said, "Send me away to my master." 55 But her brother and her mother said, Let the young woman stay with us a few days, at least ten; after that she may go.
We are not given a reason. But the request for Rebekah was sudden and ‘out of the blue’, so to speak. Perhaps they wanted time to think it over to get used to the idea, or just to delay parting with one of their family. The number 10 seemed to carry with it the idea of an unspecified number in Hebrew idiom.
For example:
Genesis 31:7 Yet your father has deceived me and changed my wages ten times, but God did not allow him to hurt me.
Deuteronomy 23:3 An Ammonite or Moabite shall not enter the assembly of the LORD; even to the tenth generation none of his descendants shall enter the assembly of the LORD forever.
We know the character of Rebekah’s brother Laban, but it is hard to discern an ulterior motive on his part here.
A mother's reluctance to part with a daughter is a possible reason.
I hope this helps.
God bless,
Glenn