I'd suggest something that is related to what you're saying: the problem isn't that "I'm a genius" is an objective statement. The problem is that a statement made with more objectivity than is warranted.
The person saying this thinks it makes him objectively better. It doens't just apply to intelligence; consider "I'm a model" versus "I'm beautiful". The latter would get negative reactions. Stating that you're a secret agent is actually an objective statement; you either are or you're not. Stating that you're a genius is likely to be interpreted as a general claim of mental superiority that is somewhat based on objective characteristics, but not by as much as you're claiming it to be.
Even if the person claiming to be a genius says "I have high IQ" instead, I've observed that people on Less Wrong give much higher credence to IQ than people outside Less Wrong. Telling an average person that you have a high IQ is telling him "I believe I am objectively superior, but I'm basing my belief on this number that is very narrowly applicable, doesn't capture all of what we mean by intelligence, and many of whose past uses have been discredited."
... more objectivity than is warranted
Oh good point. Okay. I think that objectivity might be the problem with "Hi, I'm a genius." but I'm not sure that's the problem with "Hi, I'm gifted." I'll try another thought experiment on non-objective statements:
Hmm, the problem with these is that nice, awesome, wonderful and beautiful all refer to traits that are too small in scope or too vague...
Idang Alibi of Abuja, Nigeria writes on the James Watson affair:
An intriguing opening. Is Idang Alibi about to take a position on the real heart of the uproar?
Darn, it's just a lecture on personal and national responsibility. Of course, for African nationals, taking responsibility for their country's problems is the most productive attitude regardless. But it doesn't engage with the controversies that got Watson fired.
Later in the article came this:
This intrigued me for two reasons: First, I'm always on the lookout for yet another case of theology making a falsifiable experimental prediction. And second, the prediction follows obviously if God is just, but what does skin colour have to do with it at all?
A great deal has already been said about the Watson affair, and I suspect that in most respects I have little to contribute that has not been said before.
But why is it that the rest of the world seems to think that individual genetic differences are okay, whereas racial genetic differences in intelligence are not? Am I the only one who's every bit as horrified by the proposition that there's any way whatsoever to be screwed before you even start, whether it's genes or lead-based paint or Down's Syndrome? What difference does skin colour make? At all?
This is only half a rhetorical question. Race adds extra controversy to anything; in that sense, it's obvious what difference skin colour makes politically. However, just because this attitude is common, should not cause us to overlook its insanity. Some kind of different psychological processing is taking place around individually-unfair intelligence distributions, and group-unfair intelligence distributions.
So, in defiance of this psychological difference, and in defiance of politics, let me point out that a group injustice has no existence apart from injustice to individuals. It's individuals who have brains to experience suffering. It's individuals who deserve, and often don't get, a fair chance at life. If God has not given intelligence in equal measure to all his children, God stands convicted of a crime against humanity, period. Skin colour has nothing to do with it, nothing at all.
And I don't think there's any serious scholar of intelligence who disputes that God has been definitively shown to be most terribly unfair. Never mind the airtight case that intelligence has a hereditary genetic component among individuals; if you think that being born with Down's Syndrome doesn't impact life outcomes, then you are on crack. What about lead-based paint? Does it not count, because parents theoretically could have prevented it but didn't? In the beginning no one knew that it was damaging. How is it just for such a tiny mistake to have such huge, irrevocable consequences? And regardless, would not a just God damn us for only our own choices? Kids don't choose to live in apartments with lead-based paint.
So much for God being "just", unless you count the people whom God has just screwed over. Maybe that's part of the fuel in the burning controversy - that people do realize, on some level, the implications for religion. They can rationalize away the implications of a child born with no legs, but not a child born with no possibility of ever understanding calculus. But then this doesn't help explain the original observation, which is that people, for some odd reason, think that adding race makes it worse somehow.
And why is my own perspective, apparently, unusual? Perhaps because I also think that intelligence deficits will be fixable given sufficiently advanced technology, biotech or nanotech. When truly huge horrors are believed unfixable, the mind's eye tends to just skip over the hideous unfairness - for much the same reason you don't deliberately rest your hand on a hot stoveburner; it hurts.