Family, fatherhood, honor
"My father was a bastard," he said at last. He sat straight as a sword in the saddle, and his knuckles were white, fist clenched on the reins. "Acknowledged, but a bastard. By one of the Castle Downie maids."
"Oh," I said. There didn't seem a lot to add.
He swallowed hard; I could see the ripple in his throat.
"I should ha' told ye before," he said stiffly. "I'm sorry."
I reached out to touch his arm; it was hard as iron.
"It doesn't matter, Jamie," I said, knowing even as I spoke that nothing I said could make a difference. "I don't mind in the slightest."
"Aye?" he said at last, still staring straight ahead. "Well… I do."
-- Dragonfly in Amber, chapter 40 “The Fox’s Lair”
Jamie is a man of honor - he keeps his promises, repays his debts, remains faithful to his wife. That deep sense of honor was doubtlessly instilled in him by his father, Brian Fraser - who we learn was a bastard son of Lord Lovat. A fundamentally dishonorable situation to be in.
That Brian was not honored the way he should have been made him an Outlander within his own family.
Jamie must see it as part of his mission to Lord Lovat to reclaim his father’s honor. To honor his father by keeping Lallybroch safe. To honor him by forging a relationship - however tenuous, or complicated - with the man who gleefully reminds Jamie that Brian was a bastard.
Doing all of this requires true bravery. True selflessness. True honor.
And it’s safe to say that at the end of this part of the story, Jamie has honored his father, and honored everything his father stood for, more than Brian ever could have imagined.