When you start a new family template in Revit, you may find preset dimensions.
For example, if you open the door template (Metric Door.rft), we are presented with a 'Width' dimension & a 'Frame Projection Ext' dimension in the 'Ref.Level view.
What you may have also discovered is while you can delete the 'Frame Projection Ext' dimension, you can't delete the 'Width' dimension. At least that's what it seems at first...
If we take a closer look at the parameters, we discover that out of the factory, the 'Width' parameter is marked as a 'Built-in parameter' where-as the 'Frame Project Ext' is not.
|Width Parameter is "Built-in" & cannot be edited.|
|Frame Projection Ext. Parameter can be edited.|
I don't know the reason why the factory does this, but the good news is, there is a way to delete this dimension so you can apply it elsewhere, and here is how.
Instead of selecting the dimension in the traditional method, tab to select the dimension line instead. It is the same method as deleting a dimension from a string of dimensions. The tab method will highlight the line the dimension sits on. Click this and now hit delete.