Honestly, when you stop to think about it, storms can be terrifying things. The whipping winds that can push you over or make some of the largest branches or even the trees themselves bow to them, the loud BOOM from the thunder, or the pounding rain, the crack of lightning off in the distance, all of these can be terrible to experience.
Some people are more worried about those things than others. It's ingrained in us to be afraid of what which can harm us. You have to admit, sounds and bright lights coming from the sky sound and look dangerous and are, even if some of us find them to be beautiful, as well. They're a force to be afraid of. That gets to some people more than it does others. Common sense says to be afraid of those things, so you'll be cautious of them.
In earlier years, thousands of years ago, people had less than we do now. Electricity wasn't something readily available, indoor plumbing, all that good stuff we have now didn't exist yet. Those people were outside. They had to handle the land itself to be able to simply survive. Their food was either grown or killed, by themselves, and they had to know how to take care of themselves.
Being outside posed many dangers, though, as you can imagine. The land not being able to take care of them, like the season not doing as well as they needed it to, and natural disasters, as well as large animals causing problems. In those times, things were tough and natural disasters could completely wreck everything they were doing, as well as hurt them. Storms were one of those worries because they could destroy the land, which provided for them, and could also kill or severely injure the people themselves. It was and is in our nature to be wary of storms.
Added to that, some people are reminded of things through storms. It's still a fear, but not necessarily just of the danger. For example, you have have been in a tornado and had your house destroyed or had a loved one killed by the storm. You don't necessarily have to be afraid of the storm to be afraid of the effects of the storm. Certain sounds or things familiar could remind you of those times and of the things you lost, making you afraid of it happening again.
Really, people have good reason to be afraid of storms. It's our nature, and it has protected us before and can do so now. It's just a person's nature to be afraid of what can harm them, or what they feel can hurt them, like storms.