Why is a CD-RW a read only disc? I added folders

A CD-RW is like a school-room black-board.
You can write on the black-board, until it is full, using CD-writing software, not using 'File/Save' dialogues.

When the black-board is full, you "erase" the whole thing,
and start again. When the CD-RW is "full", use the CD-writing software to "erase" the complete disk.

That "someone" may be correct: there is a way ("packet-writing") that software can allow a pre-formatted CD-RW to be used as if it were an "ordinary" writable device, e.g., 3.5-inch diskette, or USB memory-stick.

If the prefious folders were written in a "disk at once" way and the disk finalized then it will behave, as you can see, just like a cd-r - read only. Copy all your files back and next time use an different writing format  - as long as your writer is MountRainier compatible.