I get that you are having trouble understanding this; it is hard and I am much worse at explaining thing in text than in person.
What is right is universal in the sense that what is right would not change if our brains were different. The fact that we care about what is right is caused by our evolutionary history. If we evolved differently, we would have different values, wanting what is gleerp rather than what is right. The differences would be arbitrary to most minds, but not to us. One of the problems of friendliness is ensuring that it is not arbitrary to the AI either.
Aren't our desires altered constantly by mutation, nurture, culture and what we experience and learn?
There are two types of this; we may learn more about our own values, which is good and which Eliezer believes to be the cause of "moral progress", or our values may really change. The second type of changes to our desires really are bad. People actually do this, like those who refuse to expose themselves to violence because they think that it will desensitize them from violence. They are really just refusing to take Gandhi's murder pill, but on a smaller scale. If you have a transtemporal disagreement with your future self on what action you future self should take, your future self will win, because you will no longer exist. The only way to prevent this is to simply refuse to allow your values to change, preventing your future self from disagreeing with you in the first place.
I don't know what you mean by "purity of human desire".
In You Provably Can't Trust Yourself, Eliezer tried to figured out why his audience didn't understand his meta-ethics sequence even after they had followed him through philosophy of language and quantum physics. Meta-ethics is my specialty, and I can't figure out what Eliezer's meta-ethical position is. And at least at this point, professionals like Robin Hanson and Toby Ord couldn't figure it out, either.
Part of the problem is that because Eliezer has gotten little value from professional philosophy, he writes about morality in a highly idiosyncratic way, using terms that would require reading hundreds of posts to understand. I might understand Eliezer's meta-ethics better if he would just cough up his positions on standard meta-ethical debates like cognitivism, motivation, the sources of normativity, moral epistemology, and so on. Nick Beckstead recently told me he thinks Eliezer's meta-ethical views are similar to those of Michael Smith, but I'm not seeing it.
If you think you can help me (and others) understand Eliezer's meta-ethical theory, please leave a comment!
Update: This comment by Richard Chappell made sense of Eliezer's meta-ethics for me.