Yes, our worldly adoption principle is a good metaphor for election. I am glad you brought it up.
It is the parents to choose the baby, it is never the baby that chooses the parents.
A helpless baby who does not see cannot hear does not perceive cannot possibly make any choices on its behalf. And in both cases the parents are not compelled in any way to do anything at all.
Earthly parents may choose a baby for reasons other than mercy and pity, yes. But the Bible is clear that we were chosen ONLY because of mercy and pity (as was the nation Israel). Now that we understand our adoption we are to order our lives worthily, as good sons who love their Father and demonstrate it in their lives.
On a similar note, God loves the unsaved. There is no question about that. And the parables of Jesus amplify this principle. But let us understand that the TYPE of love of God extends to the unsaved is ONLY pity and mercy. On wretched vessels that have no worth whatsoever. Unfortunately for the unbeliever Gods love does have a limit and that limit is met eventually.
Contrarily, Gods love for His family members is on a different level. It is infinite, it is the love of a Father toward His sons, it will never end.