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From the moment she set foot in Westeros, it seems she is telling everyone the truth instead of lying. She spent years in House of Black and White training how to be a better liar, blend in and create a convincing cover by conjuring up stories as that's the tool of being an assassin. Lying, spying and being in shadows to get to your target. But instead of doing that Arya is walking around telling everyone what she wants to do and who's her target.

I mean look at her breadcrumbs:

1. After killing Walder Frey, she leaves all the Frey's wives as witnesses. She took of her mask, tells them who she is. I understand she wants to convey the message that North remembers, but she didn't have to blow her cover, she didn't need to show them her face. She could have just said "North Remembers" and that would have conveyed the message.


2. She tells the Lannister soldiers that she was going to Kings Landing to kill Cersei. Good thing the soldiers took it as a joke.


3. When she meets Sansa in the crypts, she tells her list and also she is going to kill Cersei. Sansa took it as a joke too until Bran mentions about it.


4. After sparring with Briene, she again indirectly says she was trained by No One. Again good thing that not many people understood what she meant.



5. 
   

   In S07E06, she trails LF 'in her own skin'. She could have put on someone else's face and trail LF but she lurked around the corner being careful not to be spotted by LF. She knew LF creates connections who do his dirty stuff, so LF doesn't need to have his eyes on her, he can pay someone to have their eyes on Arya while she has her eyes set on LF.

   
   




6. 
   

   In S07E06, Arya tells Sansa she was trained by the Faceless Men, that she can wear faces of someone and imitate their voice. She goes on to says that she imagines what it be like to live the life as Sansa.

   
   

Understandably not many people knows about the Faceless Men, about No One, about being trained by expert assassins but being an assassin is about careful. Instead of lying and keeping her skills a secret she shows everyone what she can do, tells everyone what she intends to do, tells everyone who she really is. This is opposite of what she was trained to do.

Because she has nothing to hide.

Throughout history, all great masters have preferred anonymity to credit and glory. Allow me to quote Batman here:

Ever read the Odyssey?
After Odysseus was caught by the Cyclops, he told that his name was nobody, so when he poked its eye out, and its friends asked “ Who did it?”; all that Cyclops could say was “nobody”.

Do you see the connection between this Greek myth and Arya Stark? She was trained at the House of Black and White by Jaqen H'ghar. She was also mentored in the water-dancing style of sword-fighting by Syrio Forel.

When she mentions “No One” she means all of her previous teachers, probably even the Hound. It would take quite some time to share her entire story, from how she escaped King’s Landing when her father was beheaded, up to how she became a formidable assassin herself. Because she is quite sure that she could say “No one (taught me).” to anyone without hesitating for even a jiffy. She’s sure that nobody would pose a follow-up question about “No one”. She could tell everyone the truth, and *almost no one would care enough to ask her complete story. Sansa is too afraid to know the full story. Bran already knows so he would neglect with some witty words. Brienne wouldn't believe her, and nobody would even if she told that she has Cersei on her "death-list".

*almost: Maybe Jon Snow would show interest in Arya’s skills and be curious about it.

Arya never told the wives and women of the Twins who she was. She simply stated that the North remembers and Winter had come for House Frey. Also, just because those were Lannister soldiers it doesn't mean that they're schemers and cutthroat like most that are in service to Cersei.