Honestly speaking, Arya, like his younger brother Bran, was a lively, cute, and lovable child. She wasn't as good at dressing up as her older sister Sansa, which often left people with the impression that she was "average-looking" by comparison. But from Aegon's perspective as a modern person... judging from her face shape and bone structure, this little girl was also a beauty in the making.
It was clear someone agreed with his judgment. If Aegon remembered correctly, someone in the original plot said Arya looked like Daenerys Lyanna, and also had the same blood of the wolf as the latter.
...
Haha, Aegon wanted to laugh.
[The Blood of the Wolf contains the pursuit of ultimate freedom, rich and poisonous romance, and untamed wildness. Only spontaneous trips, reckless love, endless adventures, thrills, novelty, and fun can satisfy those who carry this bloodline.]
It's also the skill of a Western fantasy author like Martin to interpret "willfulness" and "playfulness" in such a literary and fancy way. What did Arya's Daenerys do to make her "go down in history"? While engaged to Robert Baratheon, she eloped with Rhaegar Prince, who already had a wife and children!
Indeed, the marriages of Lyanna Stark and Rhaegar Targaryen were arranged by their parents, family alliances made for mutual benefit. Perhaps after meeting each other at the Harrenhal tournament, they discovered that the other was their true love and resolutely did something foolish. From a modern person's perspective, for the sake of political correctness, Aegon might even have to support them.
But that foolish girl with the "blood of the wolf," of all the things she shouldn't have done, she shouldn't have run off without leaving a single word! Aegon himself knew as early as six years old to tell his parents where he was going when he went out to play. Who is to blame when something happens if a teenage girl doesn't even understand this principle?
A Stark daughter eloping with a Targaryen Prince to become the latter's lover was originally just a scandal involving the royal family and the Lords of the Stormlands and the North. At worst, the marriage alliance between House Stark and House Baratheon would fall through, Rhaegar Prince would get another stain on his reputation, and he would pay some price to settle the trouble he caused.
But because of Lyanna's foolishness and ignorance, the false spring began. Her father and brother believed Rhaegar had abducted and kidnapped their daughter, chased after him to King's Landing to demand her return, and even spoke disrespectfully to the King. As a result, they ran into Mad King Aerys in a bad mood and were both burned to death. Then Lord Jon Arryn of the Vale refused to hand over his two wards, Eddard Stark and Robert Baratheon, and instead raised the banner of rebellion – the magnificent War of the Usurper began.
In the end, one of the eloping parties died, his name lost and dynasty overthrown. The other, after causing the deaths of her father and brother, passed away due to difficult childbirth. Those who lived could only sigh and recall her beauty from her statue... This was simply identical to Robb's later breaking of his betrothal which caused the Red Wedding.
This is the world of Ice and Fire; court death, and you will die.
***
Of course, while equally willful and spoiled, the Stark children were still somewhat different from Joffrey, whom Cersei had raised. Simply put, the Stark children were still salvageable. At the very least, they knew how to be polite, and at least they had cultivated the shining qualities of kindness, integrity, and loyalty. If it weren't for the coming chaos, and if he were just looking to make friends and find companions, Aegon would be very willing to choose these people from the North. But now, what he needed were wealthy and powerful allies and intelligent partners, and on this point, the Starks, who were skilled at screwing over friends and family, were not the optimal choice.
Not to mention, Arya was only ten years old now. This "wolf" was still young. Unless Aegon was a pedophile, who would be interested in her?
His initial thought was very simple: keep a good distance from these Starks who came with a built-in "screw over teammates" buff, and don't give them a chance to drag him down when they court death. His own swordsmanship was mediocre; teaching this little girl Arya might be enough. But if he were to take over the position of that Braavos chief swordsman, and then also inherit his fate from the original plot, that would be truly unlucky.
...
But thinking about it carefully, even if this little female wolf didn't have much skill for now, her status as a Stark child was still enough to be intimidating. He had gone to Eddard and gotten a certificate by deceiving him; this thing was usually convincing enough. But if clients frequently saw a Stark girl when entering and leaving the Night's Watch Office, wouldn't their confidence in the bonds they held be even stronger?
Furthermore, although he hadn't yet thought of the best way to sow discord between Littlefinger and Eddard Stark, no matter what plan he adopted, if he could win over a Stark child, the plan would definitely proceed much more easily.
"Hmm..." After a brief internal struggle, Aegon deliberately rubbed his chin as if in difficulty, and relented: "It's not completely impossible, but there are conditions – since you want me to teach you how to use a sword, then I am your Master, and you must listen to me."
"Okay, Master, I'll listen to everything you say!"
"Mhm." Aegon continued thinking. Suddenly, he remembered that a certain Faceless Man he had been unable to figure out how to recruit seemed to have a connection with the girl in front of him in the original plot?
There was a saying that people with similar smells are attracted to each other, just like Aegon and Tyrion. Even if the former didn't try every means to approach and befriend the latter in Winterfell, as long as they had a chance to meet and work together again in the future, they would definitely still get along. So, would this point apply to Arya and Jaqen, the old and the young?
After thinking about it, he felt that the idea of recruiting Jaqen through Arya was simply ridiculous. He ultimately decided to take things one step at a time and first bring these two together to see what would happen: "My first instruction is, from now on, don't come running to me dressed like a boy. Learn from your sister, fix yourself up like a girl, and then come for sword lessons."
"Why!"
"What's so special about dressing like a boy and also being able to use a sword like a boy? If you can be both a lady and have excellent swordsmanship, becoming a rose with thorns, isn't that more challenging?"
The above statement was just drawing a picture on a piece of paper casually. Making the girl wear girls' clothes was actually just Aegon's personal idea: he was already dizzy with busyness; how boring would it be to teach a tomboy swordsmanship when he was free? But if the other party was a girl, even if he couldn't eat her, he could at least feast his eyes and relax his body and mind, right?
"That makes sense." Arya thought hard with her little head for a while, was attracted by the idea of a rose with thorns, and agreed, "Then I'll start coming tomorrow?"
"Up to you. If nothing unexpected happens, I'll be staying here for a long time from now on." Aegon shrugged: "The second requirement is, before coming out, tell your Father or his guards and find someone to escort you... Although the Red Keep isn't far from here, you are a child, and it's not necessarily safe."
"I'm not a child anymore!"
"If you say you're not, then you're not, but do as I say. Since you want me to teach you how to use a sword, don't cause me trouble."
--
A/N: Actually, there are clues in the original work about what mission Jaqen came to Westeros to carry out. Has anyone analyzed it?