Imposibility of bias-resistant coin tossing (Cleve'86) and its connection to modern notion of fairness in Secure Multiparty Computation
First, I'll discuss Cleve's result really quickly, as there's a natural generalization of it which may be useful for your understanding.
Let $X\sim\mathcal{D}$ be some random variable.
A common notion in sampling random variables is rejection sampling. You have some predicate (function which returns true or false) $\phi$, and you want to sample $X\sim\mathcal{D}$ such that $\phi(X)$ holds.
This is to say that you want to sample $X\sim\mathcal{D}$ from the conditional distribution $X\sim\mathcal{D}\mid \phi(X) = \mathsf{true}$.
You can do this by continuing to sample $X\sim\mathcal{D}$ until you get one where $\phi(X)$ holds. This takes roughly $1/\Pr_{X\sim\mathcal{D}}[\phi(X) = \mathsf{true}]$ samples (so predicates that hold with low probability require &quot;more samples&quot;, as you'd expect).
Cleve's result is just noting that an adversary can do this in an interactive protocol via aborting the computation.
Say you have an interactive protocol where each round a single person talks (you can let them broadcast things if you want), and there are $k$ rounds.
Then in the $(k-1)$th round, there's a single participant (call them $P$) who will not hear anything from other participants during the rest of protocol. They already know what their result will be.
To show that fair coinflipping is impossible, you just need to argue that $P$ can rejection-sample on their output value until it is whatever they want it to be, so they can fix the mutually-shared random variable (at the end of the computation) to be whatever they want (but the lower-probability the result they want to occur is, the more aborts they need to do).
To show that fair computation is impossible, you just need to argue that $P$ already knows their value, and via aborting the protocol can withhold relevant information from the other parties in the protocol.
So the two results (impossibility of unbiased randomness generation in interactive protocols, and impossibility of fair computations) come from slightly different arguments, but both of them rely on the existence of one person who is &quot;done with the computation but still needs to talk to other people so they can finish the computation&quot;, which is intrinsic to interactive protocols of this form.