I truly hope you will never be in such a situation and then meeting somebody telling you that you are a refugee because of a choice you made.
Tech people often miss the social connotations such terms bring with them. Understandable, as many got into tech because of its clear definitions and lack of ambiguity and baggage, but the real world just doesn't work that way, and we have to acknowledge this.
I helped a bit as a volunteer in an orga that among other things worked with refugees and I heard their stories. Every single one had this moment that one day they have risen and took ownership of their lives, instead of succumbing to helplessness. If they didn't, they probably wouldn't make it. That is something to admire.
One thing migrants and homeless need is to recognise they're humans that are disposed to make decisions about themselves, by themselves. To deny that is cruel, because it's inhumane. Humans can make decisions, non-humans can not. I don't know how it is on other side of the pond, but over here in Europe there's a big campaign to portray refugees (and all migrants) as non- (or sub-) humans, and denying them agency is part of that effort.
I'm not sure about the exact context of the language you quoted(not a native speaker), but ISTM you mean “well it's their choice that they are homeless” as somehow demeaning. Is it used in your country as a rhetorical device to imply that a person could have just chosen not to be poor (or persecuted), and then as an excuse not to help someone in need? That's very wrong and not matching reality I saw. Usually the choice was to either flee or something even worse happens to him/her (or the family).