What makes a great trainer?

I figured a little list can be started to give an idea of what a great trainer. I partially do this because I just now found a great trainer (after 10+ years of riding!)and it makes such a BIG difference!
So if I may start (not listed in order of importance, just what comes into mind):
A great trainer:
- explains what to do, how to do it and WHY that is done (not just do this, do that, but you do this like that, because it has this effect on the horse, you and what you want to do)
-answers all your questions to the best of their knowledge and is happy to answer questions training related or just horse related in general
-cares for horse and rider
-is honest
-teach towards your own horse, I.e. Teaches you things you will be able to use inside and outside of the ring (example: my trainer is teaching me how to lunge and round pen - I have NEVER had anybody before that teach me how to do it right before and I love it because reading on this forum is many problems are solved on the ground, so once I have my own horse I will be able to apply those skills)
-can give you valid reasons for his/her training method (i.e. I use a lunge whip instead of just twirling the lunge line, because xyz, or vice versa)
-is knowledgeable not just about the riding style, but also horses in general (health, behavior, etc)

One I think of more I will post. But you all feel free to add and post your own views.

I think a good trainer should have the attributes you listed above plus:

- be an excellent communicator (to both horse and rider)
- be able to push you and your horse beyond your comfort zone without "overdoing" it

Also a good trainer can do:

-can get the horse to retain the information after many years
-Doesnt scare the horse in order to train
-Is very honest ("hey this horse isnt going to work out for this disipline...etc")
-works with your comfort zone... but tries to push
-They train because they love it... not ALL about the money
-Takes in consideration the welfare of the horse for everything that they do
-Is ethical

I know there is more but I can't think

that's probably one of the most important ones!

Patience and understanding for both the horse and rider.

I personally think that in addition to what you already mentioned great trainer knows how to do the lessons fun. I mean the trainer can be very knowledgeable and all, but the lesson can be very boring still (and I run into it number of times). And if it's a case I don't feel like doing something.

A great trainer should be able to read the horse and feel the feelings of the horse. IMO the best trainer is a horse!