SometimeSometimes, if we try too hard to soothe and ease all their emotional reactions, we wind up reinforcing them. Having your undivided attention and energy, as a child, is obviously preferable to not, and if kicking up a fuss makes you go to great lengths to "fix" that, then they get rewarded for it.
Not to say it's an intentional thing. Maybe they don't like the idea of being alone, but, as with all unknown or new things, they will resist at first, but acclimate if they have to. If they are able to get you to acquiesce instead of having to deal with that new experience, then they'll keep doing so, or even escalate.
Parents sometimes just need to develop a thicker skin about the kids being upset. They're kids, they get upset quite easily, but they also get over stuff very quickly. It's the upside to having the attention span of a child. We just have to fight our protective instincts when we know it's just about being upset vs protecting them from harm.