For instance a kid says that they are scared of storms and the parent tells them that there's nothing to be afraid of and to 'just go to bed'.

Or a kid says that they are having a bad day because they lost their favorite dinosaur shaped eraser and the parent responds with something like, 'oh you think that that's bad, wait until...' or 'that's nothing to be upset over.'

I'm 30 years old, and I'm scared of storms. The sounds of the wind blowing against a house has always scared me.

True.

The way I see it; at some point it is probably good to get a child to face their fears so that they don't get worse. But you have to be gentle about it. They won't overcome a fear or problem if you yell at or embarrass them. Also just because a problem seems trivial to an adult, these problems seem huge for a kid. It could be their first time encountering a small inconvenience or a frustrating situation and so that just makes it seem more stressful to them.