Like Eirene said, I don't think it's really about the term, but the concept behind it, and more specifically using that concept as a way to divide people into graded categories.
Dragon Lady wrote:But maybe I just feel entitled to be a first class citizen and don't realize it?
No, not exactly. What you're hitting on is the concept of social privilege, and one of the more insidious aspects of social privilege is that it's often invisible to the people who have it.
So, suppose you have two groups of people, X and Not X. And some aspect of life is harder for the people in one of those groups. But for some reason, the people who are in the easier group don't recognize that their membership in that group is making their life easier, and if the people in the harder group try to bring up the disparity, the people in the easier group may dismiss their concerns as being imaginary or overblown.
In this case, take the groups as BIC/Sealed vs. Not.
Do these groups constitute graded categories?
Yes, we hear a lot of Church rhetoric about how it's important to be sealed to your family, as well as scary stories about people who weren't sealed to their families (for some reason) and therefore don't get to see them in heaven or be with them forever.
Apparently, there are also some people who privilege BIC over being sealed later in life. From one perspective, sealed is sealed, and there are certainly many prominent Church members (especially early members) who weren't BIC. However, there are other people who prize multigenerational Mormon families, or who want to point out that their parents were married the "right" way or were generally righteous. So, basically, even if there shouldn't be a functional difference between being BIC and sealed, it's certainly something that some members could use to puff themselves up, and the non-BIC people don't really have much of a defense.
Are some aspects of (Church) life harder for one category than for the other?
Yes. Whenever you hear or read about positive examples of families in the Church, you're almost certainly reading about families that have been sealed. Whenever you read about a family that isn't sealed, it's more likely to be in a negative context (either highlighting that family as a bad example, or as deserving of pity). So, basically, in a church that strongly emphasizes family, the families of Group Not X are consistently portrayed as being lesser.
Another example is that Church leaders are, demographically speaking, far more likely to belong to the BIC/sealed category that the Not BIC/Sealed category. It could go either way with being sealed to parents, I suppose, but it seems unlikely to me that someone would be made a bishop or higher if they weren't sealed to their wife and children (so long as travel expenses weren't the only obstacle), and this scenario gets increasingly unlikely the higher you go up the chain. (Of the First Presidency and Quorum of the Twelve, for instance, I'm aware of Elder Bednar being raised by a mixed-member marriage, but his father still joined the Church when he was in his 20s. I don't know what the demographics are, churchwide, but I highly doubt that 14/15 members are sealed to their parents, spouses, and children.) The effect of this is that not only are non-sealed families not held up as a positive example, leaders of Mormon congregations aren't likely to understand firsthand what it's like to be in this situation, which leads to less support and advocacy.
Also, from a more practical perspecitve, if one or more people in your family aren't members or aren't members in good standing (which is a common co-occurrence of not being sealed), then they can't come to your wedding if you decide to have it in the temple. (And if you decide to have a civil wedding so that they can attend, then you're propagating the non-seal-age!)
Are the people in the easier group unaware that their life is easier by virtue of belonging to that group?
You and I are both BIC and neither of us can think of a time when this has come up in a public setting. Portia and Eirene could both think of examples off the top of their heads. It's possible that this has simply never come up for you and me, but I think it's more likely that it came up and we just forgot about it (as Eirene suggested).
Also, once you start to be aware of some aspect of privilege, you'll start to see more examples. For instance, I saw a picture frame in the BYU Bookstore the other day that said something like "My Forever Family" on it. Personally, I thought it was a little cheesy, but I didn't take it as putdown of my family, because I do have the "forever family" they're talking about. But if you don't, how is that supposed to make you feel?
I occasionally read the blog of a woman who isn't sealed to anyone because she's a convert (so, not sealed to parents) and she's divorced (so, not sealed to husband and can't be sealed to children on her own). She's been in some very kind, supportive wards since her divorce, but her kids (who are elementary school to middle school-aged) come home from church almost every week asking or crying about not being sealed to anyone and scared that they will be alone in Heaven. Do your kids do that? Do you think they'll ever be subjected to that pain? If not, can you see how that is a kind of privilege that you may not have been aware of?
Do people in the easier group dismiss the concerns of people in the harder group?
Yes. You suggested that they should perhaps work on "not being offended by people instead of making people walk on eggshells." (I'll acknowledge, though, that you may have been referring specifically to ever using the word BIC, but this is certainly an attitude that others have had, more generally.)
Why do we, in the Church, tend to put the blame on the offended and not on the offender? If one of your kids started using a racial slur against a neighbor, would you just figure that there was nothing to be done about it and the neighbor should just work on not being offended? Or would you correct your child's behavior? Why? And if you think that an entire culture can't be changed, try looking at media that's 50 or 100 years old for racist messages that would be absolutely unacceptable, today. Did our culture change because we told people to quit being offended or because even those of us who weren't affected by those statements acknowledged their pain and started holding offenders accountable?