The quest is not impossible, and is actually very easy. You need to coordinate your group so that you aren't all running around like chickens with your heads cut off and actually have somewhat of a decent understanding of the mechanics within the strike. Clean up mistakes like dying to stupid, standing in fire, and taking too long to kill meaningless adds. If it was impossible Bungie would change it, but as someone who's entire clan got the Rat King the first week, and could have easily gotten it every other week as well, I can confidently assure you that the difficulty is subjective and you just need more practice.