Why did humans lose their hair

I always like this hypothesis, that we lost body hair to be able to cool our bodies better when running long distance and sweating profusely. It was needed when we started hunting big animals, running them to exhaustion and to death.

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But that cannot be the whole picture. Before a preference for hairlessness began, we first had to start losing hair.

I agree with this. Sexual selection only reinforces a positive mutation, it doesn't lead to it. Positive mutation occurs first to accommodate change in environment or lifestyle.
In this case, when humans were still hairy, our sexual preference was to like hairy skin.

Interesting tidbit:

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A 2004 study found that a variant of the MC1R gene, which is known to be important for darker skin colour, was already present 1.2 million years ago.
This is telling, because naked skin would only get darker after it was repeatedly exposed to heat. The first patches of fur-free skin were probably pink, after which the tropical sun quickly pushed the evolution of dark skin. The presence of theMC1R variant suggests that our ancestors were on the path to dark skin, and therefore hairlessness, by 1.2 million years ago.