Blood Ties
It could have been said that it was all because of the blood ties, that were clearer between Arya and Jon than between them and the rest of the Stark children, but it wasn't that simple.
Jon always knew he was different - a bastard. Even if he loved his brothers as much as if they weren't just half-brothers, he still knew himself to be different.
And Arya, she just didn't fit in her role, she could never be the lady that they wanted her to be. It would have been easier for everyone if Arya was the bastard and Jon the dutiful younger son, she always wished that she were a bastard as well, not to be forced to do all those boring chores, until the day Jon gently told her that even if she was a bastard, she would still be a daughter and a woman, and expected to marry to someone to increase the family network.
But he did understand it, for he also wished to be a true son, if not for any reason, just not to be looked down upon and mocked as he often was. Jon was a serious child, and never dealt well with being teased.
And as they were parted, Arya missed Jon more than anyone, and Jon missed her as well. He wondered were she was, imagined if she had become a pretty girl, or if she had died in the bloody war that swept through the kingdom.
Arya knew where Jon could be found, and had hoped to reach him. She still hoped to reach him, even if she had accepted her other duties, beyond the sea.
She longed for him to ruffle her hair, and for the casual hug that made her sure she would be alright.
Jon was ready to fight for Arya, even if it costed his life.
It went far beyond blood ties - it was in their heart, and in their heart they knew they were never truly apart.