Dogged stubbornness, particularly about wars, was one of their central tenets. Mind you, I've read that attitude was part of what allowed Hannibal to pull his textbook double envelopement at Cannae...

It's not like the native Roman cavalry was actually bad; by what I've read they performed well enough, and for example were able to defeat superior numbers of Celtic cavalry and supporting light infantry at Telamon or some similar battle. Seemed to do pretty well in the Macedonian Wars too. It's just that the parts of Italy the Romans inhabited weren't very suited for raising horses so they were obviously quite expensive, and moreover the eques class was the incubatory of the future sociopolitical elite which gave them a vested interest in keeping the membership a bit exclusive - no point in letting future competitors in the door, right ?

So the Romans preferred to "farm out" as much of the cavalry duty as they could to the socii. This had several advantages. For one, it shunted the raw expenses of raising and maintaining the horses on the Italian subjects/allies. Second, it put a good portion of their aristocracy where the Romans could keep an eye on them and they were disinclined to cause trouble. Third, one cynically suspects, it helped to whet down the numbers of the potentially troublesome socii aristocrats in a manner that was both socially and ideologically acceptable plus militarily very useful for the Republic to boot...
And, of course, it allowed the equites and the higher social ranks that often came from their numbers to play closed club more than they could otherwise have.