That's whatam sayin!
and how might such a conflict be experienced? (thanks for playing along)
Cognitive dissonance, generally. Imagine Person A, who values the well-being of people generally, but also values feeling good about themselves and has a sense of self-esteem that's inextricably linked to the image of their country. Then imagine that Person B points to a situation in which their country is doing things that harm the well-being of people. Person A, faced with this clash of values, may pick well-being of others over personal happiness and acknowledge and criticize the policies of their country that hurt others. Or they may favor their own happiness over others' well-being, get defensive, and insist that their country did nothing wrong and whatever it did was justified.
Likewise, two of my values are happiness and honesty in every way, especially being sober about things and acknowledging uncomfortable facts. They often get in the way of another, so I tend to side with the latter, because I despise cognitive dissonance. But, you see, I
can't just abandon my values of honesty and sober thinking just because they can get in the way of happiness. I can't simply decide to ignore uncomfortable truths with the flip of the switch, and I would feel dirty if I did, which would also make me unhappy. Either way, I'm going to be unhappy.
But in any case, most of my unhappiness doesn't come from a conflict of values. It comes from a bunch of other things. So you're being hasty to claim that my values are inherently bad.