See this discussion here:
https://forums.oracle.com/forums/thread.jspa?threadID=2399658

It is unconvenient to bind the selectedToggleProperty bidirectional, since it is read only.

What you have to is, add a listener to the Toggle, you want to bind, and then manually call selectToggle().

I see no reason to make it read only.

It should be similar to the ComboBox's valueProperty()

Please check if this is appropriate. Maybe there are reasons for being read only, we don't know about.