Push is an assertion of individual authority.
Pull is a directed solicitation for collaborative buy-in and input.
Shades aims for a kind of narrative that we all know from our actual experience: two or more people were involved in a situation that turned ugly, but all of them remember it differently and - surprise, surprise - in such a way that they are mostly blameless. However, as they rethink what happened, they come around to see the other's points of view, realise the falsity of some of their own recollections, and perhaps may reconcile themselves.
Now that sounds less scary and art-pour-l'art-like than talk about unreliable narrators, doesn't it? But it is about unreliable narrators, because all the memories that the players tell us about could be false as well as true, or partly false, or multiply interpretable. And this unreliability is essential to a game of Shades, for it is only by telling conflicting stories and then partly resolving the differences that the game proceeds.
Now, what about Push and Pull in Shades? At first sight, it appears to be the most Push-like game in the world. Players narrate in turns, and during your turn you have absolute and total authority over the narration. The other player(s) cannot object to what you say; they cannot make you say anything; they cannot interrupt you, or ask for any form of mechanical resolution. You have ultimate authority to assert whatever you wish.
However, at the same time, everything you say is an invitation: "Please, if you think this is interesting, contradict me on this point. During your turn, narrate something that casts doubt upon what I have said." You cannot make someone contradict you, but you can invite her to do so.
So there is a Push-Pull duality to every statement. On the one hand, you have absolute authority to say whatever you like and add it to the narration; on the other, in order to progress, you must constantly strive to make assertions that the other person finds interesting enough to contradict.
Contradicting has the same kind of duality. You are allowed to contradict whatever you wish in any way you like (Push); but this is not enough to have the game progress. For such a contradiction is also an invitation to the other player: "Please, if you think this point of difference is interesting and should be important to the story, give me a Black Token" (Pull). Every Push is a Pull, every Pull a Push.
And of course this is essential to Shades, which is all about learning to trust each other in a situation without safety nets. It gives people the ultimate authority for pushing, and in fact forces them to push constantly; but at the same time it makes their success dependent on being able to turn these pushes into effective pulls.