[A.A. Cunningham]

Barrier recovery is what they use if the aircraft can't lower their hook.

There are many other reasons to raise the barrier if the hook won't come down. As the picture shows, that Intruder has snagged the #2 wire.

[Yo-Yo]

There are many other reasons to raise the barrier if the hook won't come down. (sic)

I'm sure you meant not just if the hook won't come down.

I don't know what all of the reasons would be, but I could guess:

1) If the arrestor wire(s) (cross deck pendants) are broken, fowled, or the arrestor engine is somehow not functioning, and it is urgent to get the aircraft down immediately,

B) If for some reason the angled deck is fowled and a missed pass (bolter?) is not possible, and again it is urgent to get the aircraft down immediately, or

III) The aircraft has made several attempts, is out of fuel, and for whatever reason cannot be air refueled to facilitate another attempt.

What are the others?