This phrase is taken from The Fellowship of the Ring, book II, chapter 1, page 265 (emphasis added):
"You needn't," said Bilbo. "As a matter of fact it was all mine. Except that Aragorn insisted on my putting in a green stone. He seemed to think it important. I don't know why. Otherwise he obviously thought the whole thing rather above my head, and he said that if I had the cheek to make verses about Eärendil in the house of Elrond, it was my affair. I suppose he was right."
Why does Bilbo say that Aragorn thought the whole thing rather above his head?