Isn’t it important to draw a line between honour and blind loyalty? For an example, take Gerold Hightower-
“As for Lord Rickard, the steel of his breastplate turned cherry-red before the end, and his gold melted off his spurs and dripped down into the fire. I stood at the foot of the Iron Throne in my white armor and white cloak, filling my head with thoughts of Cersei. After, Gerold Hightower himself took me aside and said to me, ‘You swore a vow to guard the king, not to judge him.’ That was the White Bull, loyal to the
end and a better man than me, all agree.” (Jamie)
As you see, Hightower was so loyal that he was even against OTHERS judging the king. IMO, this is just inhuman. If he had said “OK, he’s a monster but we still swore to guard him” I’d say he had some humanity left in him. This wasn’t the case.
Someone like that has the capacity to sit his ass down and watch as pyromancers burn down a city full of innocent men, women and children (forgetting that he’d ever have sworn an oath to protect them) just because a king said so. Jamie wasn’t like that. He remembered the oaths he took and saved all those lives.
He also knew that he had to protect the king’s secrets and therefore killed all the pyromancers.