In order for Fighter fighting styles to show up you have to extend your new classes tags to the existing fighting styles.
If you are timid, stop now, it's a complex multi-step procedure.
I believe there are two tags that need to be applied to each fighting style:
abCategory.XXXFigSty
&
SpecScource.cHelpXXX
XXX is the 3 letter ID you gave your custom class when you copied fighter.
I've only ever figured out how to do it by copying an existing style and getting the tags set up and then marking the style Obsolete (so it doesn't show up in the list), so the process I used goes like this:
1. Go to the Class section of the editor, choose the Custom Ability tab.
a. Copy an existing fighting style, like Archery (doesn't matter which).
b. Find the Special Ability Category button and click on it.
c. Choose the top checkbox for - New Tag -, hit OK and a dialog will pop.
d. In that dialog type the ID XXXFigSty where XXX is your class ID.
e. In the Name section type CLASS Fighting Style, where CLASS is the class name (like Fighter, Swordmage, etc.) Ignore Abbreviation.
f. Hit OK
g. Click the Available to Classes button.
h. Find and select your class, hit OK.
i. On the far right choose the Tags button.
j. Click the Click to Add Another Tag link.
k. In this dialog: Group ID = Helper, Tag ID = Obsolete.
Save and test this ability. The two tags are now live and set up.
Go to the General section of the editor. Select the *Extend Thing tab.
You will need to create two extends for each fighting style you want to extend your tag to. So when you hit New (Blank) you will need to hit the Find Thing button and find the fighting style. It will auto fill in the Thing Unique ID field, on the group ID type SpecSource and the tag ID you will need to type your class ID - should be cHelpXXX where XXX is that 3-letter ID.
Repeat and this time group ID is abCategory and the tag ID is XXXFigSty.
You can test now! these extends but each time it forces you to reload the game system. Once you repeat this for every fighting style the styles will start to show up.