Phase out means that zoos will stop breeding a species and simply let the population die out naturally. The goal of phase out is to see the population go to zero. This can be done for one of several reasons.
First is a local phase out. A zoo has simply decided they no longer want the species for whatever reason and will let their population die out or transfer it all away. The dhole are an example of this. They thought it would be easier to get more after our innitial aquisition and now most dholes in North America releated to ours or soon will be. Getting more from India has been proving difficult so the zoo decided to just let Patty and Martha live out their lives at the zoo and then replace them with a different species. Theres new hope in getting more dholes so its not a North American wide phase out yet.
Second is that zoos have simply lost interest in the species. Each Taxon Avisrory Group, or TAG (elephants, felines, canines, bears, ect) puts out a survey to its members to evaluate the spaces available, threat to the wild populations and interests in each species that falls under its domain. They then try to maximize the effectiveness of their space. This is extremely complex. In the TAGs in which Tur, Tahr, babary sheep, Chamois and european mouflon belong there either wasnt enough interest in keeping them, need to keep them, or the space for them would be better served keeping other species. With the Mouflon they have decided the better option is to switch from European Mouflon to Armenian Mouflon.
The third reason for phase out could be medical concerns for the population. The populations genetic diversity could have dipped below acceptable limits and are concerned about the effects of inbreeding, think white tigers and white lions. Or there is a disease they are concerned about, for instance the barbary apes are on phase out because they can carry some sort of disease that can be transmitted to people. Not that they are all diseased its just proven a concern that has turned a lot of zoos off the species.
A fourth reason could be they are trying to keep the bloodlines pure. Bengal Tigers have been phased out for example because they were too often interbred with other tiger species creating generic tigers. Or hybrids like in the orangutan population. Sometimes though they just ignore it as with the Reticulated/Rothschild Giraffes or Asian Elephants or all ostriches. Probably depends on the chances of creating pure lines.
Theres other reasons but those are some of the biggies. Most important one being either a local or contiental lack of interests.
The zoo has plenty of other phase out species. Its just Eurasia seems to have the highest concentration.