One of the biggest lies we tell is not having favorite kids:

It’s one of the worst-kept secrets of family life that all parents have a preferred son or daughter, and the rules for acknowledging it are the same everywhere: The favored kids recognize their status and keep quiet about it. … The unfavored kids howl about it like wounded cats. And on pain of death, the parents deny it all. …

384 sibling pairs … [were] questioned … and videotaped … as they worked through conflicts. Overall, … 65% of mothers and 70% of fathers exhibited a preference for one child, usually the older one. … “The most likely candidate for the mother’s favorite was the firstborn son, and for the father, it was the last-born daughter. ” …

Firstborns have a 3-point IQ advantage over later siblings. … Kids who felt less loved than other siblings were more likely to develop anxiety, low self-esteem and depression. (more)

Interestingly, lying here is seen by many to signal caring:

Not all experts agree on just what the impact of favoritism is, but as a rule, their advice to parents is simple: If you absolutely must have a favorite (and you must), keep it to yourself. Even if your kids see through the ruse, the mere act of trying to maintain it can help them preserve the emotional pretext too — a bit of denial that does little harm. What’s more, the effort it takes to tell a benign lie is in its own way an act of love toward the unfavored child.

Its not clear though how often disfavored kids see self-serving denials as showing care. Do parents who care more about disfavored kids actually lie more than others?

Also, we less resent favoritism to lower status siblings:

Even the most blatant favoritism is easier to take when there’s a defensible reason for it. Perhaps the most extreme example is when one child in the home has special needs. Children with Down syndrome or autism … Kids with physical disabilities … require more time and attention from parents … Talking about the situation openly is the best and most direct way to limit resentment. … “Research suggests that differential treatment may have no negative effects when children understand why.”

Oh kids understand favoritism toward smarter, prettier, stronger siblings – they just hate it more.

I suspect that many commonly told lies are accepted and even encouraged because they are seen by many as showing that liars care. Cynics who tell the truth are, in contrast, described as cold and hostile. A problem, of course, is that we often believe our lies, leading to mistaken inferences and decisions. Which may be why humans often seem so oblivious to “obvious” implications of their “beliefs.”