Just one man’s opinion (mine).
I think it must have something to do with the promise God made to Abraham, a promise having to do with “seed,” his descendants. Women don’t have “seed,” the promise had to do with male issue, the men of Abrahamic descent. Hence, the putting of the hand of Abraham’s servant “under my thigh.”
The promise made to Abraham’s “seed” being the overarching theme, it is thus no wonder the strange custom you refer to. Strange to us, perhaps, but not to Abraham’s household.