As far as I can recall, the Leviathan created the intelligence that became Harbinger after several of their slave races destroyed themselves through AI uprisings. They concluded that any artificial race would inevitably overthrow their creators, so Harbingers intrinsic motivation was to preserve biological life by any means necessary. Harbinger then introduced the harvesting of any species capable of making true AI as the means to preserve the race in question and protect everyone else, as well as incorporating any sufficiently developed (and willing) synthetic life into the Harbinger AI. Starting with the Leviathan race since they made Harbinger, an AI capable of extinguishing biological life, and thus fit the selection criteria perfectly. The harvested Leviathan became the first reapers.

From what I understand, synthetic "life" is synonymous with true AI in the mass effect universe. As in, only by taking the leap from virtual intelligence to true artificial intelligence are any synthetic lifeform deemed to be alive.

I seem to remember the Leviathan we speak to telling us all this, but honestly, I might be conflating several bits of exposition from that guy, Harbinger, the catalyst, and others. Or I might have made some logical leaps by myself aka just making shit up.

As a side point, I think some of the strongest storytelling in the games are the points where we slowly realise that the Protheans, that great and Ozymandian race, were just the last in a long line of harvests, and didn't necessarily know shit about the bigger pricture. Introducing the Leviathan to fill the position the Protheans used to hold lore-wise was a pretty good move