From what I have read online, some people like the idea of furry as a hobby, something they do for fun, something they do when they are bored, or just something that they can do with friends. Furry is an artistic hobby, too...some people like the imagination.
Furry might be a daily visit to a website, a drawing of your fursona, an art trade, a conversation, a dream, a passing thought, a medium for expression, or just part of a multitude of hobbies you may have.
But, from what I have read, some people attribute more to this particular hobby. In fact, to them, it is more than a hobby, ranging from a daily interest to a way of life (or an imagined way of life). To them, they identify with anthros for some reason. They may also express this by wearing a collar or a tail, but to them, it is an idea that they wish to live. Some turn to dreams, maybe stories. But to them, it is very much a part of themselves, an deep interest. I've seen some people who wish they could see what it would be like to live in an anthro body, for the feeling of inhabiting a body other than their own...
And to some, this interest may be a bit abnormal...
I honestly don't see a need in coming out on your own terms; if someone asks, just tell them what it is.
But for others, who might take it a bit more serious, who knows...they feel the need to come out like a non-straight person feels the need to tell his family that the charge doesn't always repel itself. Maybe for them, it's a liitle more than furry.
And for the furries feeling the need to come out, it can be caused by a lot of things. Maybe it's a way of getting attention. Maybe it's because you want to feel accepted. Maybe you enjoy being open, or you want to refrain from being closed. Maybe, this hobby is being blown out of proportion. Who knows?
Let's just enjoy it