Re: I'm not an angel. I'm a panda!
I'm not sure that such statements are more common amongst the angel-kin folk than not - but if so, could be caused by a number of reasons. The first being that it just doesn't come across one's mind as (pardon the term) easily as some other kin-types out there. Most may agree that angels are an energetic being, not a physical flesh and blood being, and thus would be vastly different from how physical being feel. It's perhaps easier for the human brain to guess at what a wolf feels/senses/perceives, but how does an angel feel? How does it see and think? I think it's very different from what we're used to - our minds just convert it over into as best as we can understand, images, metaphors, etc (which is why many angelkin are winged human sorts, even though that concept of angel is relatively modern).
The stigma could also be connected to it, both the common perception of Angel and the term of angelkin - for the most part even within the angelkin grouping there's something of a subculture - choirs, cherubs, etc.
*edit* I also think that angels being vampiric make sense on some level - angelkin are further disconnected from their original "source" and so may need to replace the energy that they would typically have.
"Justice, like lightning, should appear, to few men's ruin but to all men's fear."