That’s a great question, I’m no expert on the situation so let me see what I can find.

The Houthis emerged as a Zaydi resistance to Saleh and his corruption in the 1990s led by a charismatic leader named Hussein al Houthi, from whom they are named. They charged Saleh with massive corruption to steal the wealth of the Arab world’s poorest country for his own family, much like other Arab dictators in Tunisia, Egypt, and Syria. They also criticized Saudi and American backing for the dictator.

After 2003, Saleh launched a series of military campaigns to destroy the Houthis. In 2004, Saleh’s forces killed Hussein al Houthi. The Yemeni army and air force was used to suppress the rebellion in the far north of Yemen, especially in Saada province. The Saudis joined with Saleh in these campaigns. The Houthis won against both Saleh and the Saudi army, besting them both again and again. For the Saudis, who have spent tens of billions of dollars on their military, it was deeply humiliating.

• Who are the Houthis, and why are we at war with them? (This source has more historical background on the political situation before and after the quotes too, but it’s too much to summarize with more quotes)

Since Yemen’s revolution ended in 2012, the Houthis have demanded a greater role in the government and in the drafting of a new constitution. They accuse the government of corruption and oppose polices they say are at odds with their minority group’s interests, including a proposed division of the country into six federal states. They say such a move would weaken their Zaidi sect’s political representation.

• 5 Things to Know About the Houthis of Yemen

It seems like they began as a resistance to US and Saudi interests and corruption in Yemani Government. It could be fair to frame the genocide as a ‘punishment’ for their resistance against US/Saudi interests in the region