There are many animals in breeding programs all over the world, the location of the which having little to do with said program. I'm not sure, i'd need to check but I do not think this bird was bred in captivity, I suspect it is more likely to be a rescued bird.
The purpose of most programs is to (hopefully) successfully breed for release threatened or endangered species, back into what is their natural habitat. Where possible and practical, the offspring of the breeding pair will be released in carefully controlled programs, with minmal human conditioning. Obviously the down side of this is that the original birds will become so conditioned to human contact that they cannot realistically be released.
In centres like the one that this Vulture has been lost from, they also serve a secondary role of education and this particular bird, like many from true "Falconry" centres, fly daily under the supervision of their dedicated handlers, much to the awe and delight of many members of the public who would otherwise be unable to see them in action. This in itself is no good reason to hold a bird captive, but it is an interesting and useful bi-product of what many see as a necessary evil. The birds get their required exercise, and they are encouraged to work for their food.
It's not an ideal situation, but the recent (relatively speaking) reintroduction of Red Kites and White Tailed Sea Eagles to parts of the UK show the value of the sacrifice captive breeding birds make.
Captivity may technically be the correct word, but these birds are far from caged in frustration.