Concept Question for Secure Computation
As in the linked question, what you are missing is that the simulated view for a given input pair must be indistinguishable from the simulated view for the same input pair.

So if $A$'s input $s$ is $0$, then the real view of $B$ will be $0$ with probability $1$. On the other hand, if your simulator just chooses a uniform bit, the simulated view of $B$ will be $0$ with probability $1/2$. That's distinguishable, so your simulator doesn't work. (Same if $s=1$ of course.)

A slightly more involved argument shows that any simulator will have the same issue, so there is no suitable simulator, and the protocol is not secure.