We would never say it but we certainly show it: We value ourselves more than others.
Western culture is individualistic, and I've seen the injustices wrought from this mentality in colleagues that are willing to trample the good reputation of another as long as it means getting a promotion for themselves.
Let's face it though, our culture bids us to demand our rights. Our culture bids us to consume recklessly and achieve the American dream even if it is at the cost of someone else.
We would never call ourselves superior but we certainly live as if we are. I believe this is why the commandment "Love your neighbor as you love yourself" is indicative of how in tune Jesus was with the culture of His time. No one ever really had a problem loving themselves then, and no one really has a problem loving themselves now.
The cure to superiority is to find our identity in the gospel. The gospel says "Christ came into the world to save sinners, Christ lived the life you should have lived and died the death you should have died and then rose from the dead"
This immediately rids the soul of superiority because our rightful standing before God is free not earned. Only when our rightful standing before God is earned can we feel superior and look at others as inferior. But when it is free and an act of grace on the part of God it is absurd to feel superior because we didn't earn it.
Believing in the gospel also rids us of any superiority complex because God came to save sinners. God is not just on the side of a nation or on the side of a particular ethnic group, but He came to save sinners.
Revelations 7:9-10 "After this I looked, and behold, a great multitude that no one could number, from every nation, from all tribes and peoples and languages, standing before the throne and before the Lamb, clothed in white robes, with palm branches in their hands, and crying out with a loud voice, “Salvation belongs to our God who sits on the throne, and to the Lamb!”"