It was some sort of a competition inside our species, probably sexual.
I'm not sure about that. Be very skeptical of claims that something evolved due to sexual selection, it tends to be the default explanation lazy evo-psy people reach for when they can't immediately think of a better explanation.
Wait, what? What are even the alternatives? The only alternatives are environmental pressure - food, predators etc. But such an environmental pressure affects a lot of species at the same time and for this reason, most traits in the animal kingdom have the expected normal distribution. Such as the ability to swim amongst mammals - many can swim a little, some better, and a few really well. Yet the distribution of intelligence in species does not follow normal distribution. Humans are far, far ahead from the species in the second places (apes, dogs, dolphin...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.