Jesus taught that we would have to answer for our actions. This is not lack of responsibility.
Also, Jesus commended His mother to the care of St. John. And does this sound like someone who wants us to abandon people?
34 Then the King will say to those on His right hand, ‘Come, you blessed of My Father, inherit the kingdom prepared for you from the foundation of the world: 35 for I was hungry and you gave Me food; I was thirsty and you gave Me drink; I was a stranger and you took Me in; 36 I was naked and you clothed Me; I was sick and you visited Me; I was in prison and you came to Me.’
37 “Then the righteous will answer Him, saying, ‘Lord, when did we see You hungry and feed You, or thirsty and give You drink? 38 When did we see You a stranger and take You in, or naked and clothe You? 39 Or when did we see You sick, or in prison, and come to You?’ 40 And the King will answer and say to them, ‘Assuredly, I say to you, inasmuch as you did it to one of the least of these My brethren, you did it to Me.’
Therefore, he did not lack care for families.
Hitchens has an axe to grind, so inviting him to a debate is not something I'd do in the first place. It's not a debate, it's cant.