Some like the term anthro more because it is more descriptive: anthropomorphic = humanoid. But people also want to move away from the term furry because outside people have tainted the term with misconceptions. You and so many others seem to have the misconception that furrys only like the art and races due to sex. Only a small percentage of the furry population are into that stuff but you see it a lot more because people from the outside find it funnier to point it out and usually drag said art out from it's intended audience to flash it in front of the unintended audience. What does that result in? Misconceptions.
Similar to how people think all anime is big titty ladies when the reason you see so much of it is because it is what is imported to the west, because sex sells. It's better now but it was a huge focus on hentai back in the day.
Can also point out the amount of regular hentai to furry porn is huge but no one screams about that and all the weird 'regular' fetishes. And trust me there are a lot of weird fetishes out there much weirder than furries.
Most furries just like to dress up, meet friends, go for a drink and just chill. That's the majority of what furry conventions are. But for some fucking reason people only want to see the small percentage that differs from that and paint the whole community in the darkest shades of fucked up. And furries know when the uninitiated use the term it's usually in a negative light.
Imagine you own hobby being branded as weird without anyone actually caring to look into what you do. You know, like gamers and roleplayers used to be, or anyone that did anything that was considered nerdy.
And again, werewolves are like one of THE most popular furry creatures. In many ways you can say it started with them. Just because not all of them look like someone gave a dog rabies doesn't mean that it isn't true.
In fact, here is an example of a monstrous werewolf fursuit:
https://www.deviantart.com/qarrezel/...wolf-646344958
And here is another by the same artist:
https://www.deviantart.com/qarrezel/...wolf-598669996
And if you look at their gallery you will see they do everything from the pretty and cute to the gnarly and monstrous, and the furry community is the same. Some like it realistic, others like it cartoony.
People have been fascinated with human/animal hybrids for thousands of years. It's not a new concept and it is part of human curiosity about the world around us. For some people it's refreshing and liberating to be able to become something you are not, even if it is just for a little while, one of the reasons why cosplay, roleplaying and larping is so popular. And for many the reason we play games like WoW and FFXIV.
I hope that explained it better.