Full Idea
If we generalise what Kripke says about the Queen, then he is arguing that the parents of any organism are essentially the parents of that organism.
Gist of Idea
Kripke argues, of the Queen, that parents of an organism are essentially so
Source
report of Saul A. Kripke (Naming and Necessity lectures [1970]) by Graeme Forbes - The Metaphysics of Modality 6.1
Book Reference
Forbes,Graeme: 'The Metaphysics of Modality' [OUP 1985], p.133
A Reaction
It strikes me that we have to be extremely careful in specifying what it is that Kripke is saying. I take it that either Kripke is saying something rather uninteresting, or he is saying what Forbes suggests. Parenthood is essential, not just necessary.