Prince doesn't know how to take care of somebody. He was lost for everything that has the definition of warming someone. Prince never hugged tightly, or even embraced someone. It was never his thing to touch someone else aside from himself.
Just now, he couldn't explain this feeling. Why his heart ached for a while, that he has been longing to do it? Prince broke off a lot of promises after meeting Aria, and it's getting hard for him to recover. To get back on his feet was something he was never done to deal with.
Prince doesn't like to recycle the plans he discarded in the first place.
Aria was a plan, and he's nearly disregarding it. Prince wanted to end it as much as possible. Pushing her on the edge of the cliff was the only solution he had inside his mind. Aria trusted him too much. Prince should have run away the moment he saw her bleeding.
What good the connection they both have if one of them was pulling the other to death?