Everything is complicated, so there's no simple coherent explanation you could have provided, but it's probably not completely valid to depict the Houthi resistance as an anti-democratic uprising; rather, they may have started as a political response to the Saleh administration, which in turn violently (and anti-democratically) repressed the Houthis themselves, who militarized in response. The Arab Spring factors heavily into this too. It's a total mess.

The one thing that does seem pretty clear in all this is that the Saudis should not be bombing anyone in Yemen.