“Families” is absolutely more warm and human than “people” and while I see what you’re saying that “people of Gaza” could be interpreted as more inclusive than saying “Gazan families”, that would be an excessively literal reading, it is really not what’s going on here.

Again, this is just one instance of a consistent pattern among media and public figures in general. Not interested in splitting hairs with you over your personal interpretation of the one specific phrase. It’s like a dog whistle, once you know what it sounds like, you can hear it, but it will escape your notice until you learn about it.