But why can you not introduce new values by wanting to want new values?
You can, it might be a bad idea (for some senses of "values"), and if you believe that you are doing that, it's not necessarily true, even though it might be.
I'm not saying that it's not possible to be correct, I'm saying that it's possible to be mistaken, and in many situations where people claim to be correct about their values, there appears to be no reason to strongly expect that to be so, so they shouldn't have that much certainty.
Many people see themselves in various groups (member of the population of their home country, or their social network), and feel justified in caring more about the well-being of people in this group than about that of others. They will argue with reciprocity: "Those people pay taxes in our country, they are entitled to more support from 'us' than others!" My question is: Is this inconsistent with some rationality axioms that seem obvious? What often-adopted or reasonable axioms are there that make this inconsistent?