This is a bit convoluted so bear with us.
Part 1: Suki
Right after Aang defeats Ozai and takes away his Firebending, Suki leans over Ozai and asks if Aang “finished the job”. Aang says that he found another way to restore balance, by taking away Ozai’s bending. We don’t see Suki’s face until Sokka walks over to taunt Ozai, but as he’s doing so, she’s looking down at him with a thoughtful, concerned expression. We submit that this is where the idea was planted within Suki - that benders weren’t dangerous if their bending is taken away.
Part 2: Ty Lee.
At the end of “Avatar the Last Airbender”, we see that Ty Lee has joined the Kyoshi Warriors. She says that after she taught them a bit of her Chi blocking, they became best friends. Immediately after Suki see’s how Aang dealt with Ozai, she lets a former enemy into the Kyoshi Warriors because she has the ability to take away a bender’s abilities.
In Korra, the Equalists are a group of people who use Ty Lee’s chi blocking techniques, and wear masks.
Masks vaguely reminiscent of Kyoshi facepaint.
Reminiscent in the kind of way that an entire group might be distorted over a hundred years. Both in their style and in their philosophy.
Ty Lee joining the Kyoshis is interesting because she joined the circus in the first place to avoid being part of a uniform group.
So here we see that she’s overcome that insecurity, and begins to see the merits of unity, and uniformity. The Kyoshi warriors become a force on par with benders, with their newfound chi-blocking abilities.
The speculation: After the war, Suki and Ty Lee begin to form a new philosophy for the Kyoshi Warriors, both influencing each other. Over time, the Kyoshi Warriors become the Equalists - perhaps the Equalists are a faction that broke off, but the Kyoshi Warriors are their origin.
Part 3: Toph
Its entirely canon that Toph has a little crush on Sokka. Suki was entirely aware of this.
In the same moment that Aang gives Suki the idea for the equalists, Sokka and Toph both taunt Ozai with the biting wit and sarcasm they’re known for. Suki, trying to fit in, tries to say something and comes up with:
“Yeeaaaah! Or how about king of the…guys who…don’t win?”
To which Toph responds,
“Leave the nicknames to us, honey”
This builds an insecurity in Suki. We already know that Suki has a tendency to be jealous in her relationship with Sokka.
Photo credit: sokkaxsuki.tumblr.com
Sokka spent so much time travelling with powerful benders. Why wouldn’t he choose them over her? This eats at her for years.
As the Kyoshi Warriors move more and more towards becoming the Equalists, Sokka states his discomfort with their new direction. Suki turns back to that insecurity, and paints the situation as a dichotomy she hopes Sokka will understand: Its us or them. Regular folks against Benders. Come on, Sokka. Its always been you and me, we’ve always been the odd ones out in the group. Y’know…
…Sokka refuses to see it this way.
They break up.
This cements Suki’s beliefs and galvanizes the birth of the Equalists.
Sokka, meanwhile, turns to the one member of their old group who shared his skeptical humor, the same girl he held close to him on a Firenation airship when he thought Suki was dead, with a crystal clear conviction that he would not lose her as well.
And so you have:
I LITERALLY COVERED MY MOUTH TO KEEP FROM FUCKING SCREAMING
HELP HELP THIS IS AMAZING