I’d assume it’s mostly a product of who the enemy was during the Cold War. Though I understand the far right made a large shift in how decentralized they operate around the end of the 20th century too after the feds started picking a lot of various KKK and other organization members off.
None of that's true. But we should be aware of the lies being told, at least the ones told widely.
"Antifa" is less of an organization than even some loose collective like "anonymous"
Are there left-wing agitators? Sure, black bloc and other "direct action" protestors have been around since at least the world trade protests in the 90s.
But to the best of my knowledge there isn't really a formal "antifa" organization to dismantle or anything.