OK some of my reasons.
I keep the Ancient Type of Hebrideans, which are very rare, although the 2 horned modern type are now not rare but are under the general umbrella of the RBST. The Ancient Type form a tiny proportion of the national Heb flock.
Our initial reason for keeping Hebs was that someone dumped them on us
. We had Jacobs and wanted to concentrate on them. We put the Hebs to the tup, but it was the Jacobs which needed cosseting and assistance for their lambing. The Hebs were pretty much ignored and lambed in their field without any help at all. This brought us up short, and made us notice their other good points. The usual good mothering, good birthing, good feet, milky, long-lived, hardy, good teeth, independent and self-sufficient, able to defend their lambs from predators to a large extent, and of course stunning to look at. Oh and surplus stock which goes to the butcher is amazing for taste.
The only other rare breeds we have kept, Shetland and Soay, are also Primitives, with many of the same characteristics. We have never kept non-Primitives of rare breeds so I have no opinion there.
We do keep our Hebs for the conservation of the breed, and in particular the conservation of the Ancient Type of Heb, which appears to have much wider genetic diversity.
The reason this diversity is important is because both our climate and our animal husbandry techniques are necessarily changing with time. Breeds which were new and developed to suit the husbandry techniques and tastes of 30 years ago may now be becoming less useful. Currently, many sheep require high inputs of medicines and care. However, considered cross breeding with a now rare breed which carries desirable traits, such as lower shepherding input, fewer feed supplements, shearing and so on, will help to develop new sheep more suited to current needs.
Rare breeds do need to be kept pure to preserve this genetic diversity, but they also should be used to develop new modern breeds which will be better adapted to climate and inputs. We tend to think that these breeds should be preserved for 'the future', but part of the future is now.