The Fire Nation has hurt you.
She wants to be closer to him. He can tell; she doesn't exactly try to hide it with the way she reaches out for him as if they didn't just meet a few hours ago. She can sense he's in pain, and she wants to comfort him. To let him know he's not alone. To connect with him.
They're both lonely. They could both use a little comfort right now. He wants to thank her, to indicate in some way he appreciates her efforts, but there is no point. Where would it lead? Even if the circumstances were different, if they had time to properly bond, it couldn't lead anywhere. But he can't tell her that. He can't tell her why it would never work out between them.
Fire. The element of power. The element of desire. The element of passion. Air, water, and rock come from the earth. Fire comes from within. It flows through your veins, always burning, always desiring to be unleashed. Your every heart beat is a spark. Your emotions are its fuel. Desire. Passion. Fire. There is none without the other.
Only those who share fire in their blood can share their passion, can share their heart, and share their bodies. Love is fire. Those with fire in their veins can feel their lover's flame and not be burned. Fire is death to humans who do not possess it within. Only those who share the gift can bear the touch of fire.
Was this the reason the Fire Nation always set itself apart from the other nations? Because its people could never fall in love with anyone except its own? If they did, they could never know each other like lovers.
It wasn't. It was simply the way things were.