No one wants to jump onto a sinking ship. Common sense dictates that people run away from and abandon sinking ships.
In this case, the Purple Flower sect is a sinking ship and no one wants to go aboard it only to go down with it. However, that won't be the case if the Blood Skull sect decided to assist the Purple Flower sect.
If the Blood Skull sect decided to work with the Purple Flower sect, they will no longer be a sinking shop and will have a chance of victory against the Red and Blue Fire sect. This chance of victory will make it worthwhile for them to help the Purple Flower sect.
If all five sects work together, it is highly possible that the Red and Blue Fire sect will be repaid. It is unlikely that every sect will work together wholeheartedly, but Arthur's job is to make it look like a possibility.
