It's impossible to "hate the sin and love the sinner."
At least that's what I've been told. Repeatedly.
Let's be honest: Not everyone who hates the sin loves the sinner. And sometimes the love is buried very, very deep.
But it's not impossible. Everybody does it all the time. Especially parents.
Yes, the best example of hating the sin and loving the sinner is child rearing. We hate certain behaviors. We want better than that from our children because we want better than that for our children. Parents ground, spank, and occasionally even kick out their children because they love them, because their deepest fear is that the child will not become the man or woman they could be.
And we can oppose — even strongly oppose — behavior in other people because we want better than that for them.
Of course, one reason people don't believe in this is that too often we only appear to hate sexual sins. Sexual sin in destructive to the sinner. So are gluttony, greed, pride, and gossip. If we love our friends and family, we won't turn a blind eye to those sins either.