Kurapika was fighting another opponent, If he could catch the man in front of him, he might be able to get a clue as to where the Phantom Troupe was, He couldn't (and didn't want to) miss this chance, He would have to train more and more if he lost here.

At the same time, the opponent was using you as a hostage, after you had been weakened in battle, Kurapika would have to make a choice, let the enemy escape and save you or let you die and he can catch the guy, He sighs, abandoning his current fight to save you, He easily gets rid of the guy who was using you as a hostage and picks you up in his arms.

"I would never let you die" he says bitterly, he really wants the troupe's valuable information, but abandoning you is like abandoning himself