Spontaneity of an exothermic chemical reaction When the process is exothermic (ΔHsystem​&lt;0), and the entropy of the system increases (ΔSsystem​>0), the sign of ΔGsystem​ is negative at all temperatures. Thus, the process is always spontaneous.

It is easy to prove this using the formula of Gibbs free energy, but how can we prove it by logical reasoning?

I was thinking that in an exothermic process, the system loses heat. Shouldn't "the loss in heat" normally cause more ordering of the system and eventually a decrease in entropy? Might be a stupid question, but what am I missing here?
Not all reaction is like this but, exothermic reactions are usually spontaneous because molecules always want to be more stable. So by reacting to another molecule and releasing energy, they can lower their own energy thus making them more stable and unreactive.