Life is indeed complicated. What fueled Iran's involvement in Yemen was Saudia Arabia invading it. They worked very hard to keep the Houthis at arms length prio

Life is indeed complicated. What fueled Iran's involvement in Yemen was Saudia Arabia invading it. They worked very hard to keep the Houthis at arms length prior to that because as different religious sects go the only thing they really have in common is that the really nasty fundamentalist women-hating Sunni sects (ie the Saudis) hate them both for being different. And what kick started the war in Yemen? That would be a daddy's boy prince wanting to prove he could win his own war without daddy's help (that went well). None of which would happen if we didn't really enjoy selling guns to the Saudis, on account of all the money they've taken from us when they sold us oil. And we'd still be happily selling arms to the Iranian King we installed if they hadn't got sick of it and thrown us out. So this is on us. All of it.