They had just met, and have known each other for only five minutes.
The Doctor had been pretending to be from the International Police under the usual name "John Smith" when he had ran into the man who called himself "Castiel." He found it odd for both of them to be on the same strange case of "Missing People." (He had believed it to be some kind of alien, or, God forbid, Weeping Angels.)
But he was even more surprised by Castiel's appearance.
He seemed to be the only one who could see them. When they had each received a copy of the case file and had read over them, the Doctor kept glancing at them when the other wasn't looking. They were majestic and absolutely beautiful.
When it came time for them to depart, the Doctor shook Castiel's hand in a friendly way.
"It was nice to meet you, Castiel. Oh, and before I forget," he leaned in very close, flashed the other a big grin, and whispered, "Your wings are magnificent."