Endothermic and exothermic reactions
Your idea is in principle correct. The reaction you mentioned works well, you break one H-H bond and create 1 C-C bond (triple bond, in fact) and two C-H bonds. The energy is released. And in most crude approximation it also says where the activation energy barrier comes from - you have to break a H-H bond.

As for the paradox - that is the principle of chemistry, to make bonds we wish for. If it means increasing the energy level, thus being less favored by nature, you have to pay for it. By sacrificing other bonds. Those are the highly reactive chemicals humbly stated above reaction arrow, which quite often do all the magic.

As the most revealing example in this I consider the Nucleophilic Acyl Substitution reaction, where you have a series of derivatives of increased stability. You can always and simply make the more stable out of the less stable, having wide choice of reactions. And there are just a few to climb up, using very nasty chemicals.