The first thing you need to remember is that "latifundia" is not an ancient term, it is a modern one coined to describe an agricultural system that people in the nineteenth century thought looked like New World slave plantations. Secondly, where we actually have evidence, particularly North Africa, Asia Minor and Egypt, "latifundia" as you teacher probably talked about them did not exist. Wealthy landowners did own massive tracts of land, but they were not worked by large slave gangs, rather by tenants and rent paying peasants. So in most respects, a Roman "latifundia" was substantially more like a Medieval manor than a New World plantation.

This is not to say there were no slave run plantations, just that they seem to have been vastly overemphasized in the literature by authors making a rhetorical point.

A good account of this is in Kevin Greene's Archaeology and the Roman Economy.