While I don't necessarily disagree with this completely, I'm not sure that this is stated correctly. Perhaps we should not love our children because of who they are, but because of who we are.
I've never known anyone who has lost their life in a rescue attempt of another, but I imagine it would take great love and respect of the life of the other. The Lord loves us so much he was willing to do this. When we accept Christ as our Savior and give our lives to Him, our goal is to be more like Him. Part of being more like Him is to love others, all others, as He loved us.
I love my children, my husband, my mother, my father, as a reflection of the love that Christ is loving me. If He didn't love me as much as He did I would probably be incapable of loving others in a life-long, self-sacrificing manner, but I am, and I can, because He does!
Praise the Lord for a Agape Love! The love He shows me everyday. The love I should be reflecting to my family and all that I see.
Perhaps the tweet and I are both incorrect. Perhaps: We love our children not because of what they do, but because of who He is!