Does anyone know if there is some limiting factor in the Feature Class to Feature Class tool's dialog that inhibits the movement of entries in the Field Map list up and/or down? I've even gone so far as to try a small polygon feature class with only 2 fields (beyond the standard OBJECTID, Shape, etc. fields which I am not transferring because I'm happy to have them regenerated in the new feature class I am creating) and the list still doesn't update when I try to move the second field up above the first. No error given; just nothing happens. I've also tried making the new feature class anyway, thinking that perhaps it just wasn't being updated in the GUI...alas, no joy!
I am working in ArcGIS Desktop 10.4.1.
If this is a bug, I'll contact support to report it.