There are not many prayers that go against our culture more than this one. We are bombarded day after day with the gospel of self, that we need to do what makes us happy no matter what. It's this message that tells us that what matters most is what we feel and what we want. Many people feel like God (if there is one) has no right to mess with their plans, or He is just another source to help them get what they want.
I love the resolve of this Psalm. This verse begins with a passionate decision. The psalmist, representing the people of God, proclaims that the glory and fame for who they are as a people does not belong belong to them, and they won't try to take it.
"Not to us, O LORD, not to us…" Honestly, that is a resolve we have to fight for. Our hearts naturally want to say, "All to us, yes, all to us!" Throughout the Bible and throughout history, this tendency has played out again and again. People look to themselves instead of God, and therefore, people crave glory for themselves rather than seeking to give God glory.