Barbs sometimes need to be removed from the run of barbed wire because the barb is in a spot close to a gate or somewhere where people may get clothes hung up on the wire.
Or, you may be using fencing posts with a clip installation system and the odd barb is too close to the post so it won’t go into the clip.
But most of the time it’s when you need to join the wire due to a break.
One of the best ways to join barbed wire is with Crimps. This makes for a strong joint so you don't need to wrap the barb round itself many times.
With some breaks you can join the wire without having to use a separate piece of wire. You just need to re-strain it then join the wire with a crimp on the overlap.
However, to keep the tension on the wire you will more than likely need to remove the odd barb on one side or other of the join if you are using a separate piece of wire to span the break.