Consider you graduated from college many years ago and you run into a friend from college and she says that Alice loved you when we were students at college. Alice was your classmate, and we can also assume she is not interested in you anymore.
So how do you describe that you did not realize/did not know, up until now, somebody liked you in the past when your talking about it with another friend.
When we were classmates, Alice would have to have loved me.
But I am not sure.
Second scenario could be:
Your mom says when you were an infant you always wanted to play with the cat at home. Of course you don't remember this.
How do you describe this situation to somebody else.
Could it be
When I was an infant, I would have love to have played with the cat.