Our reasoning behind Volatility Skew is summed by one of the main findings of Prospect Theory, for which the Economics Nobel was given to Kahneman and Smith in 2002 is that people tend to be more risk seeking when down and tend to be more risk averse when up.
A real life example of this many can relate to is increased risk seeking when losing in poker vs. decreased risk seeking when up.
The same magnitude of loss hurts more than the same amount of gain is pleasurable (or relatedly, missing out on greater potential gains), so people will act to minimize losses and lock in gains.
Prospect theory can help explain why volatility skew exists. According to the theory, people are more sensitive to losses than gains, and therefore, demand a higher premium for lower strike price options that offer downside protection.