Dean saw Cas’ wings when it was whole, years later he saw it on the ground, burnt, broken, almost featherless. And a thought came to his mind:
“I did it all for you.”
“Don’t lose it over one human.”
More than anything, he’s the one who broke Cas, cause all of this to happen. He led an angel to fall from grace, and never did once tell said angel how really grateful he is. He never really told him what he feel.
“I love you.”
He looks up to the sky as he remembers this, he slowly realize that his feelings for the angel are more than what he thought they are.
And now he prays to Chuck, mind spinning countless words and not stringing them into coherent sentences.
He just wants Cas back.
But heaven is silent, and he sees the broken wings once again. He traces the lines on the ground, it occurred to him that he never once asked Cas about his wings, of what would it be like to touch them.
He’d lost the chance to annoy Cas about this, it would have been funny to run around the bunker following Cas and grabbing the back of that stupid coat, stubbornly telling the angel he wants to see the wings.
He’d lost the chance to tell Cas that he loves those wings even at their current state. He loves them as much as he loves Cas.
He’d lost the chance to return that “I love you” in words.
He looks at the burnt wings because he can’t look at Cas. He looks at the charred remains of Cas’ wings as a reminder of how broken he is right now.