Do coaches have to be "Better" than those they coach?

Do coaches necessarily have to be  "Better" than those they coach?

Most people often confuse or link coaching with teaching and training.
In teaching, we always believe and expect our maths teacher to have all geometry theorems and riders on their tip of the fingers.
We expect our trainer to be an expert on the subject he is imparting the training.

This implies that the person performing the coaching is better than the person receiving coaching.

They are nearly always more experienced no doubt, however particularly in sports they may not be "better" than the player they are offering coaching.

For example, the number one ranked player in tennis will not have anyone better than him in the world at that moment and yet they still receive extensive coaching from his coach.

Does it make some sense?

Why would the number one ranked player in the world listen to someone who is not as good as him and still it is equally true that his coach surely can teach him a thing or two the player still don't know.
A coach gives him a few tips which the player is not aware of.

That's why Coaches not necessarily have to be 'better' than those they are coaching.