After Cassian knew where Galen was, he didn’t have to go back for Jyn when she was on that platform. He had no orders to bring her back, nor did he have to go and get her before leaving Jedha. He didn’t even have to keep her alive after finding out that Galen was on Eadu. In fact, the smart thing would have been to leave her on Jedha, or put her out of her misery so that he could complete the mission without further complication.
She was expendable at that point, and not imperative to his orders. She was a liability, because any reasonable person knows that she wasn’t just going to stand aside when she had a chance to be reunited with the father she hadn’t seen in 15 years, who sacrificed himself out of love for her and for the sake of the rebellion. Cassian especially would know better than that. The smarter thing would have been to dispose of her just like he disposed of the informant on the trading outpost.
He couldn’t even pull the trigger to fulfill his orders because of Jyn. He not only knew in his heart that Jyn was right, but he couldn’t hurt her like that. “I had every opportunity to pull the trigger, but did I? Did I?”
He even tried to call off the Rebel Squadron on Eadu because “Jyn’s on that platform!” At that point, she was entirely irrelevant to his orders, but instead of running away from the fight, chaos, and distraction, he runs TOWARDS it to go get her and save her from the Alliance bombs. He wouldn’t leave her behind, or let her get hurt beCAUSE HE LOVES HER.
→ The White-Gold Tower, also called the Imperial Palace, is the enormous central spire of the Imperial City, located in the heart of the Palace District. The tower was built by the Aldmer in the middle of the Merethic Era and was the center of the region occupied by their kin, the Ayleids. Currently, it serves as the Imperial Palace and hosts the vaults and libraries of the Moth Priesthood. It can be seen from all over the Imperial City and the surrounding countryside, and is a defining symbol of the Empire.