When I'm asked to be a mind reader, the only technique I know is to ask.
Humans are unique as a species because, as you demonstrate so well, they have an unconditional drive to discover better (Unconditional) qualities (such as Truth, Knowledge, Beauty, Justice, and Love).
I can't take credit for making this demonstration, or even understanding it. I don't know what "unconditional drive" means. I assume that what you mean by "better" is that humans value things. So I think what you are saying is that humans are unique because they have a drive to form values.
If humans kill humans, the dead humans suffer unconditional, irreversible harm to their ability to be human. Therefore humans have the right to life. All creatures of human origin have the right to life because they are human. Otherwise, some of those unique creatures may suffer unconditional, irreversible harm.
Here again I don't know what you mean by "unconditional". But, I think you are saying that humans have a right to life, because without life they irreversibly cease to be human. Therefore humans have a right to whatever prevents them from irreversibly ceasing to be human.
So by combining the above, I think I can distill your position to:
'A thing that has a drive to form values has a right to whatever prevents it from irreversibly losing that drive.'
Do I understand you correctly?