What? There are interactions that can never occur because they're forbidden by the laws of physics - you'll never violate conservation of [energy, baryon number, momentum, etc.] even with probability 10^-14.
But if the reaction is the least bit reversible (and most are) then the reverse reaction is still proceeding even though the forward reaction is stronger. It's just doing so at an incredibly low rate, and the products are likely to be immediately converted by the forward reaction.
You are looking at averages and claiming they hold for every single event in a stochastic simulation. Taking the example of entropy - it's not impossible that entropy decreases in a system, it's just less likely than it increasing. On a stochastic level, entropy decreases all the time, it's just that on average it increases more than it decreases.
Reactions work the same way. You're not actually making chemicals react as a singular act, you're creating a forward reaction that occurs more rapidly than the reverse reaction.
If we had a hypothetical chemical Maxwell's Demon - you could "bottle" up the tiny bits of those outputs from the reverse reaction before they underwent the forward reaction again.
For example particle accelerators can shoot particles against some target one by one, and so there's no need to look at averages. Some interactions never occur, to the best of our measuring ability (i.e. highest energies and number of repetitions). Some others are right away forbidden by laws much stronger than entropy in thermodynamics, in the sense that they're not averages, but mathematical derivations off the symmetries of the universe.