I think this is more of a complaint rather than a question that can be answered.
For example "Why is there..?" can only be answered by that moderator who was involved.
What gives them the right to do so?
the answer is because he is a moderator he can delete as he is empowered to do so. Whether fair or unfair another issue.
Why and HOW are they still occupying the mantle of moderator?
I mean how can one answer this.. it can sound a bit harsh but is this the first time you have encountered a moderator whose workings have been unfair? I have seen many such moderators in other forums.
But, the problem definitely exists and i can say that from my personal experience.
Keeping exactly this issue in mind i had posted earlier this question - Can comments deleted by one moderator be restored by another?
So, from the answer it is clear, the other moderators can see all those deleted comments. If they also feel that deletion was unfair then they can restore the comments.
Or, if you yourself notice you can also raise the issue in the chatroom called "Moderation". The other moderators can then look into it.
Since, the mods are the only persons who can see the deleted comments, consulting them first (before posting here) makes sense. If the other mods also say that the deletion was fair according to them too, then of course posting here is the solution.
But, the real problem here is that we can't really know when our comments are getting deleted. So, it is fairly cumbersome for us to keep a track of the situation (by going to the "all action" tab we can check but that's exactly how it is cumbersome).
Here, i have just given a practical solution for the problem. IMO, situation is not that bad now, like how it was previously, when there was only one decision-making mod. As i have seen one mod (of the current group) undoing what was done by another on several occasions. So, we can expect fair moderation now.