In terms of swordsmanship level, Aegon might not even be half as good as the chief swordsman Arya's Father originally hired, but teaching a girl with no foundation the basics of swordsmanship isn't a duel, so a higher skill level doesn't necessarily give an overwhelming advantage.
Aegon still clearly remembers that his middle school physics was taught by a physical education teacher... It sounds like an outdated joke, but it's true. When he was in middle school, his parents were busy starting a business, so he attended a small, broken-down school in his hometown. In that small campus, except for Chinese and math teachers who were always present... they needed to recruit for everything else. His homeroom teacher was a young woman who had just graduated from a physical education college, and she taught both physical education and physics for the entire class.
The physics level of the homeroom teacher, who came to the profession late, could be described as extremely low. She taught while self-studying and preparing lessons. He can still recall the often-hilarious situation in class where the homeroom teacher would correct errors she had made in the previous lesson. But interestingly, even under such extremely backward and poor conditions, the class's physics scores were consistently far ahead of the other two classes taught by teachers who graduated from normal universities.
For Enlightenment (enlightenment/initial instruction), extensive knowledge is not the decisive factor. More important is whether the teaching method is engaging, whether the content is easy to understand, whether the teaching attitude is proper, and whether a good example is set with dedication and effort—if a solid foundation can be laid for students and their interest in learning can be cultivated, then as an Enlightenment teacher, one is qualified.
Admittedly, that homeroom teacher and physics teacher who graduated from a physical education college could absolutely not teach anyone high school physics, but the way she seriously taught and patiently guided and answered every student's question remained firmly imprinted in Aegon's mind even after he graduated from university with a degree in physics. Even today, he still believes that the person he encountered back then was the 'best' middle school physics teacher.
***
Now, he was about to play the role of Arya's Enlightenment swordsmanship teacher. Although his skill level was average, he believed that as long as he was serious and patient, he wouldn't teach worse than Ser Alliser.
Aegon agreed to the girl's request to learn swordsmanship with the most direct goal of establishing a good relationship with a member of the Stark family, and thus more conveniently benefit from Eddard's status as King's Hand in case of need. With a clear objective, he naturally wouldn't be as strict and meticulous as the dance master from Braavos in the original plot... He didn't play tricks like throwing a sword to see if she could catch it. He very properly handed the girl a lighter training sword and taught her hand-by-hand how to grip the sword and stand. The lesson began just like that.
Arya was left-handed, which was quite interesting. According to something he had heard before crossing over, the reaction speed of the left hand is faster than the right. Perhaps she was naturally born to be an excellent swordswoman.
"There is no such thing as a great swordsmanship in the world, only countless sword techniques and defensive and offensive movements: thrust, chop, hack, sweep up, bash, clear... these are for offense; dodge, block, parry, deflect... these are for defense." Aegon, being unskilled, didn't dare to mislead his student. He only spoke of principles he had heard from Gared and Ser Alliser Thorne that were absolutely correct and universally applicable: "What a swordsman needs to do is learn and master these movements and techniques, and know when and in what combinations to use them."
"We will start by practicing the most basic movements, building a solid foundation. When the time is right, you can decide on the techniques and style that suit you best."
Aegon began teaching the girl the most basic sword movements. Perhaps there were hundreds or thousands of people in the world who could perform these movements more beautifully and skillfully than him, but they wouldn't necessarily teach Arya better. Aegon had only started learning swordsmanship over a year ago. At this moment, this weakness became an advantage—he still clearly remembered the difficulties and doubts he encountered during the getting Started (beginner) process, and the solutions he eventually came up with. To the Night's Watch's surprise, this little she-wolf learned incredibly quickly, so much so that she soon asked to learn new moves.
"How long do I have to do these movements?"
"You can't do them too long. These are the most basic movements. Do you want to run as soon as you learn to walk? If you think you've got it, try attacking me."
After a series of clanging exchanges, Arya didn't even touch Aegon's clothes.
"This skirt is so annoying! Can I take it off?"
"No. Overcome the difficulty. You are a girl, a lady of the Stark family. There will be many occasions and times when you need to wear skirts in the future. Will your enemies give you a chance to change into pants?"
"Hmm... Why do girls have to wear skirts? Pants are so much more convenient and comfortable!"
"Don't blame the skirt! Come on, keep practicing!"
"It's not fair! This sword is heavier than my needle!"
"It's much lighter than a real sword! And, do you plan to use a needle your whole life?"
...
Amidst Arya's grumbling complaints about her skirt and the training sword, they practiced until lunchtime. After eating something, Aegon proactively suggested a break. There was no need to rush the progress. Whether the girl could handle a larger training volume was one thing, but Aegon was afraid she would learn too quickly and he would run out of ideas within a month.
They returned to the inner office, relaxing in chairs and chatting. As 'master and apprentice,' they had only met a few times before and didn't know each other well. And for Aegon personally—he still hoped to quickly improve his relationship with the Stark girl through a few heart-to-heart talks, just like he attracted Tyrion's attention in Winterfell by rambling that day—the content, of course, was tailored for this playful and willful little girl, using "China" as a template.
...
Completely as expected, Arya was quickly attracted by the carefully woven lie. What Aegon told the girl was naturally not the advanced technology and systems of "China," but the concepts of gender equality and the free and open atmosphere that were most lacking in the Ice and Fire World: in that distant country west of the Sunset Sea, girls could openly learn swordsmanship, could enter the army through normal channels, and even become government officials... and perhaps most importantly for many girls—they could choose their own husbands, and even demand a divorce if they were unhappy.
If it were just these things, it would at most make Arya yearn for that fictional country, but when she heard that Aegon had come to Westeros and become a Night's Watch member after an accident during an adventure around the world, the girl's eyes immediately lit up.
"You are an adventurer!" The girl's wolf blood almost boiled. Perhaps it would be more appropriate to say her chuunibyou spirit was burning fiercely? Aegon instantly became her new idol: "When are you going home? Take me on your next adventure!"
"Heaven knows when I can go home. There are no ships in Westeros that can safely cross the Sunset Sea."
"Oh, I see... Okay, then tell me more adventure stories!"
"Not practicing swordsmanship?"
"Later, no rush."
The girl's interests changed so quickly it caught him off guard. This was a bit of a minor problem. Making up stories about China was easy, after all, in a sense, Aegon did come from "China," but he wasn't a real adventurer... Of course, he hadn't eaten pork, but he had seen pigs run. He had loved reading fantasy and adventure novels since he was a child. Searching his memory, picking some out and processing them into his own material wasn't difficult for him.
Just as Aegon was weaving a story, Tyrion's voice suddenly came from outside the door: "Aegon, come out and receive a guest! The first bond buyer is here!"
—
[T/N: 绝境长城上的王者 by 点爷01 is a proper ASOIAF / GoT fan-fiction, so expect lengthy chapters about political intrigue, medieval warfare, and world-building. However, this is not to say that there are no action-filled chapters as well, so enjoy the show.]