Fat person: "Look at me, I'm fat."
Not fat person: "Look at me I'm fat."
The first could be self deprecating and cute. The second guy is being a total offensive dick.
In one case it is true and the other it is not.
I strain to see the offense.
If a fat person is offended because a non-fat person calls themselves fat the fat person has a problem besides obesity they need to deal with.