Regardless I think you have a moral obligation to tell your employer why you cannot extend.
You’re at work and they need you to go from over here to over there.
I think you really only have fatigue as an “out”.
Because you don’t feel like it just doesn’t cut it in my book.

Now...here’s the caveat.
If your employer is equally ethical in their duties, Scheduling and planning and dispatch in trying to avoid an extension....
Some are not though.
I’ve flown for an operator that would schedule 4 legs within 5 min of max FDP.
Expecting you’d sign an extension prior to leg 4, knowing you always incur delays that you can’t make up in a 45-60 min leg.
Now it’s pretty much emotional blackmail as you’ve got an airplane boarded and ready with people that need to go somewhere and a cabin crew that wants to go home.
Good luck being the a-hole that walks off.
I do think you need to be flexible enough to extend if it’s really unforeseen.