This warning is triggered when loading family files into the project from the Modify tab while you are placing elements, and the category of the family you are attempting to load does not match the category of the elements being placed.
Warning: Some or all of the family files you selected cannot be loaded. You must choose family files of the category <Component>. Do you want to retry loading a new set of files?
Issue: When you load a family from the Contextual Tab of the Ribbon after you have started a placement command (i.e. Door, Window, Column, etc…) the family selected for loading MUST match the category of the placement command. If the category of the family you are trying to load does not match, you will receive the warning and the family will not be loaded.
For example, if you select Architecture > Door to begin placing a door and then you select Load Family from the contextual menu, you can only load door families. If you load a family from any other category, you will receive the warning. The same rule applies for all of the placement commands in Revit.
Solution: Be sure there is not a category conflict when loading families into your projects. You can do this in 2 possible ways: