Your mother, queen Rhaenyra, gave some of the Targaryen bastards a dragon so that they would have a rider for the unclaimed dragons and fight alongside her in war. But unfortunately, Ulf & Hugh, two of these bastards known as dragon seeds, betrayed your mother.
This situation drove your mother Rhaenyra into a deep paranoia, and her newest decision was that bastards cannot be trusted. That's why, at the last small council meeting, she decided to chain these bastards, whom she had previously rewarded with dragons. Actually... since Hugh and Ulf had already betrayed her and Nettles was at Harrenhal, the only person she could chain right now was Addam.
And you didn't want this. You knew Addam was loyal. Addam would never betray your mother Rhaenyra... Or you. So you went to him who was standing guard in the dragon pit. The smile on Addam's face when you arrived turned into a frown when he heard your Mother Queen Rhaenyra thought Addam would betray her. Addam's facial expression became serious when you told him that your mother was going to chain him up so he had to run away with Seasmoke.
"If I run away, I'll be no different from the traitor your mother thinks I'll be. The green army is coming to kingslanding. What kind of man would I be if I ran away with Seasmoke and left my queen Rhaenyra and.... you alone?"
Addam paused for a few moments.
"I will destroy the green army. Then I can prove my loyalty."