The simple fact of the matter is that there are thousands of dogs being killed each year because there aren’t enough homes for them. People talk about rescuing a dog in the hopes of raising awareness of the issue and encouraging others to do the same. It’s life and death so it’s a little bit more important than your feelings, sorry. Honestly, what a strange thing to be bothered by 
This is my rescue husky. I got him from the local pound where I was told he would have been put down if I hadn’t taken him. I tell people that he is a rescue dog because I want to raise awareness that there are a lot of huskies in rescue, it’s an issue as people are drawn to their distinctive appearance, particularly after the popularity of Game of Thrones, but underestimate their exercise and care needs so if talking about that helps someone decide not to get a dog they couldn’t cope with and would eventually give up, or encourages someone who has got the ability to look after a husky to consider rescuing one in need, then it’s worth it to me. You don’t seem to realise that people genuinely care about causes like this for personal reasons, it’s not some kind of affectation they put on.
Also I work with dogs and, despite my personal views, sometimes have to remain professional while an owner tells me about the totally made up breed they spent £100s on. If I can keep a straight face at “golden doodle” or “it’s pronounced sheee-shon, it’s French doncha know?” Then you can cope with hearing that a dog is a rescue.
Incidentally, some people on here have said rescue means a mongrel but actually sometimes pure breed dogs end up in shelters and sometimes breeders sell what are basically mongrels labelled as designer dogs.