Ishvi didn't actually get the reference to Icarus, mythology was not something he had much experience with, but in his conflicted mood, something in the sentence struck a chord. "I can't fly in the sunlight or I do burn." That was part of his shame, already slower and weaker than the full angels, he couldn't just sprout wings and fly. He had to shift, turn into a creature with black wings, who couldn't handle the light of day. No way for anyone to tell he wasn't fallen, except his words.
And that half, the nightmare half that he tried so hard to deny and dismiss because he knew it made him less, that was what he really wanted to show her. Because the story had hurt a little, but even if he never told the whole thing, it wasn't much of a secret. It was just something he'd done, a little piece of futility.
But this was one place, flying under cover of night where he shifted voluntarily. "I know people have seen me in my other form. I can't really control it when I'm ... stressed. But I try not to do this in front of people. I train it alone as much as I can. I don't fly where people can see me. I - I have black wings. I don't look like an angel."
Ishvi didn't expect her, or really anyone who wasn't an angel from home to know what it meant for him to show this to someone. He wasn't really looking for sympathy, which may have been one of the reasons he wanted Phoebe there, someone who wouldn't try to fix him. Actually, he couldn't have said how he expected her to react except possibly by glitching.
The change was quick. Shadowed form blending into the darkness so well he might be hard to see, black-feathered wings unfurling. He took off without waiting for her response, launching himself over the ocean - faster than walking but slower than a bird. Ishvi didn't go very far before he stopped and threw the plane into the ocean rather than trying to fly it. Then he returned to the beach and curled his wings around himself self-consciously. He didn't want to be the one to break the silence.