The military follows the orders of the president. They aren't fighting to kill or destroy the Houthis because that, apparently, isn't Biden's goal. Biden's presidency has been almost dovish in its approach to conflicts, which has been highlighted in Bob Woodward's excellent book War. This is the guy who argued vehemently (though unsuccessfully) against the troop buildup in Afghanistan when Obama was president.

His administration has always focused on diplomacy and limited engagement — as we've seen with his approach to arming Ukraine — so it shouldn't come as any surprise that he doesn't want to invade Yemen and eradicate the Houthis.