Well there are two thoughts perhaps three on how the Society got it start.
1. Coyote. Now BattleTechWiki citing various canon sources seems to accuse Coyote as being the source of the Society which began with the Versailles Pact. Little is known of this agreement which peacefully bought this Babylonian city into the Clan during Operation Klondike but it is speculated that these were the seeds of the Society which took root. The Clan's close proximity to the Society on Tamaron and its eventually collaboration with them during the Wars of Reaving could be powerful evidence in this theory's favor. Link below;
http://www.sarna.net/wiki/The_Society2. Wolverine. In the link below JPArbiter and myself had a great exchange regarding the Society. He proposes that the Wolverines began the organization following the Annihilation when sterilized scientists absorbed into other Clans may have been able to spread their ideas. Don't know if you ever saw Captain America Winter Soldier but it is sort of like Hydra after the 2nd WW using Operation Paper Clip to work for the west. This does make a certain amount of sense and for evidence just look at former Wolverine possessions like Circe which is a hotbed of Society influence.
https://www.ourbattletech.com/forum/index.php?topic=2831.msg38287#msg382873. General Movement. Perhaps neither of those factions or any Clan is directly responsible for giving birth to the Society. Scientists could have come to the same conclusion on their own after watching how the warriors ruled them for several years. Hey we should be in charge is a very human reaction to totalitarian rulers who allow no outward political dissatisfaction to creep up. There are numerous historical incidents were the warrior caste brutalizes the lesser castes and the intelligenca could easily say hey we can do better.
Another theory I have is Widowmaker could also be a culprit as another disaffected faction absorbed into the Clans following their destruction. Ironhold is another stonghold of the Society and it was a Widowmaker world but it could have really been a combination of all of these factors. Disaffected scientific personnel who in at least two cases may have been sterilized could have wanted to sow the seeds of rebellion eventually and started pouring poison in the ears of anyone who would listen. While we may never know for certain it is all quite plausible.