Let me start by saying that I love Arya and I am personally rooting for her to murder everyone still on her list.
When Bran gave Arya the dagger from Littlefinger I grinned with glee.
And then when she showed up to practice with Brienne with both Needle AND the dagger, I was literally bouncing in my seat.
It showcased all the lessons she learned from Syrio Forel, Jaqen, the Waif, and the Hound.
It was an amazing fight... but I have some beef.
You cannot parry Brienne's sword with a smallsword!
I'm sorry, but it's not possible! Now, if Needle was enchanted with super strength somehow, this would make sense. But I'm pretty sure it's just a regular smallsword Jon gave her.
I should also say that in high school and college I had a very nerdy hobby.
I used to like to go to stage-combat workshops up and down the East Coast hosted by SAFD (the Society of American Fight Directors).
Now, I know that doesn't make me the biggest expert in weapons in the whole world, but I do know a couple things.
Smallswords are designed for one thing, and that's speed.
The weapon Brienne is practicing with is built very differently.
Even if Arya had the beefiest arm in the world and was much stronger than Brienne (and come on, is there anyone in Westeros stronger than Brienne?), Needle still wouldn't have been strong enough to block the force of her sword.
Now, I still believe that Arya could've won in a fight against Brienne.
I think Arya is fast enough that she could've water-danced circles around Brienne and tagged her before Brienne could've landed a blow.
She even proved that earlier in the episode when she dodged the guards at the gate.
But being able to block Brienne with a smile on her face? I'm sorry, but...not today.
TL;DR: If Arya had tried to parry Brienne with Needle it probably would've broken.