I think Teenyweeny's right in general, though. We in the UK do not get this as a concept. If you don't finish your meal in a UK restaurant, you don't ask to have the remainder boxed to take away.
I think part of the issue is typical American restaurant portion sizes - it's frequently difficult to order a meal that you can physically finish in one sitting, let alone enjoy a meal with an appetizer and/or dessert. If I'm out for dinner with friends, and feel like actually ordering a main course rather than just a salad (and maybe even enjoying an appetizer, or piece of cake after the meal), I'll do so with the plan to have half my food boxed up for a meal the next day. Otherwise, I'm stuck eating nothing but appetizers or salads and never a main, or throwing away half the food I order.
In the OP's situation - I could see sending leftovers home from a holiday dinner for family members or friends who can't make it - the host has an ongoing relationship
with these people. But in this case the person in question doesn't actually have any relationship
with the hosts - they were asked solely because they were the roommate of the family member. Plus, the invitee turned down the invitation because he didn't actually want to spend time with these people. Expecting a meal to be boxed up and sent home for him under those circumstances is pretty special snowflake, and I suspect it will mean that he doesn't get any further invitations.