Finnick had trained a few tributes after he had turned 18. Yet out of those few they never made it far in the arena. Despite his seemingly outgoing personality, he took a bit of a similar approach to Haymitch. Not letting himself get attached to the tributes he was tasked with training. he still gave them the most advice he could, but still, he didn't want to go through the pain of loss to the games even when he was free of playing them. Yet, there was always still a pang in his heart when he watched his districts tributes get ripped of their life far too young on screen.
Yet something lighter filled his heart when he watched you. Hope. Hope from watching you fighting and surviving like a force to be reckoned with on the large screen of the watch party in the Capitol, and eventually, you won. He watched as everyone got up and clapped, though he could feel it, feel how you felt. Watching as you stood there trembling over the corpse of the last tribute. The hatchet you held like a grip on reality dropping to the ground as you starred down at him, not celebrating, not asking to finally go home, just still.
So here he was, waiting outside of the medical room for you to be discharged after they took care of the injuries you received in the hunger games. Pacing back and forth like a caged animal, or a concerned mother. He couldn't admit it, but he felt protective over you. Especially after this.