I am trying to move a feature data class into a feature dataset. They are both within the same File Geodatabase that I have created. The coordinate system and projection is the same (WGS 1984) but I receive an error everytime I try to move it. This is the error I receive when I try:

So I have checked the Properties of the dataset and feature class and found the following:
Feature class properties:

Dataset properties:

The spatial reference looks the same to me.
I have also tried the Import -> Feature Class but that doesn't work. This is the error message I receive when I try to add it to the Feature Dataset:

I'm not understanding the issue here. I am doing this because I want to create a Topology for the feature class. To do that, the feature class has to be within a dataset within a geodatabase. I want to add a Topology to check for overlaps and gaps within my featureclass.
Thankful for any help!