I think there are a couple different definitions of "gifted" being conflated here. One, the concept of high intelligence, and two, the general sense of being talented. Almost everyone has talents and "gifts" in that sense, but not everyone is intellectually gifted. No value judgment there, just a statement of fact. Not everyone is a natural athlete, not everyone can draw in perfect perspective, not everyone can invent original recipes that taste good.
I see the difference between talents and giftedness thusly: A person can learn the rules of a sport or art and--even if they don't have a natural ability for it--with a certain amount of work they can learn to imitate or approximate a talent for it, even if it's a really crappy approximation. Exhibit A: The "art" you see on motel walls.
However, intellectual giftedness cannot be approximated. You have it or you don't, and although you can abuse your brain and get "dumber," you can never get any smarter than you already are. I believe THAT is why the subject is so touchy. It goes against our ingrained societal belief that if you just work hard then you can get better at anything and do anything you want. Well, you can work all you want at getting smarter and it will never happen. The most you can possibly do is train your brain to work a little more efficiently within the limits of your natural intelligence. Sadly, this last notion is what seems to drive the majority of the "gifted and talented" programs in our school systems, which does little but mess up people's perception of giftedness and produce a lot of miserable busy-worked stressed-out kids.
I do agree with some others here who have said the label is being overused--you are absolutely correct. See the end of my last paragraph. However, I do think there is value in the label for those kids who really need it. If nothing else it lets parents connect with each other. I know I found it to be a huge help when I discovered there were other kids like mine and some who were even more "out there"! The sense of relief was enormous. If I hadn't had a "label" to type into google I never would have found that support.
I guess it can be hard to understand that just being smarter can be any kind of a burden or special need. I mean, wouldn't we all love to be able to think a little more clearly or remember better or whatever? And it doesn't seem very important, does it, how smart a person is, as long as they are content. But that's the thing with a truly gifted child--they are often NOT content because their brains are racing this way and that and all around in ways most of us literally cannot imagine. They get overloaded with stuff most of us don't even think about. For instance, when my son was around 5 he was reading an astronomy book and broke down in tears for half the night because "the universe is so big we'll NEVER learn everything about it." Another example: A few months ago we were talking and my son said how he was doing something differently (at a different time) than the other kids in his Y class did it. I tried to sympathize and said "I know, we all feel different sometimes." He replied, "I don't feel different sometimes, I feel different ALL THE TIME."
Those are the kinds of comments that send parents looking for support. It's not all about when a kid learns to read or whatever, although very early milestones can be a shock to a parent who hoped (like most parents) for nothing more than a healthy baby. Giftedness does have its own set of symptoms and challenges--it's not an imaginary thing cooked up by overambitious parents. Honestly, I never even thought about "giftedness" or about how smart my kids would be. I guess if anything I assumed they'd be a little above average like most of my family, but it's not something I pondered. It took me a long time to come to grips with the fact of my son's high intelligence and how it wasn't something that would resolve itself without attention. Comments about him being "weird" "freaky" "scary" etc did NOT help.
Sorry to hijack, but I'm just trying to address a few of the comments I've read on this thread and hopefully help some people to understand why support for gifted children and their parents can be necessary, even in a homeschooling environment.