O2+2H2⇌2H2OΔH=−125.7kJ(4)

What side of the reaction is favored? Because the heat is a product of the reaction, the reactants are favored.

I believe you are confused. The reaction 2H2 + O2 ==> 2H2O is favored to the right (products favored). Delta H is not the defining contributor to a reaction. It is dG = dH - TdS. So if dH is negative and dS is + then dG will be negative and dG = negative number is a requirement for the rxn to occur spontaneously. In many cases where dH is -, as in this case, we can speculate that dG will be negative but that isn't always true. Your logic is not correct.