It is easier to look at history and experimental observations, then try and make the math work. Historically, one of the early attempts to come with criteria for spontaneity came from Berthelot in 1867. He proposed that all exothermic reactions are spontaneous. Yet, we know that there are some spontaneous endothermic reactions and processes as well. For example, boiling water is endothermic, yet it is spontaneous. There are other examples as well so they came to the conclusion that :delta:H<0 is not an all inclusive requirement for spontaneity.
Now if you look at the Gibb's free energy:
:delta:G = :delta:H - T :delta:S.
you can see that T :delta:S is a correction to Berthelot's hypothesis. We are saying that exothermic reactions that have a positive :delta:H will be spontaneous. Also, endothermic reactions with a large positive :delta:S will be spontaneous. So now spontaneity depends on both the breaking and making of bonds as well as entropy. There is a competition between entropy and enthalpy. In addition, temperature comes into play. Bond formation is spontaneous when it is enthalpy driven, even though it is disfavored entropically.
Hope this helps some.