Question: I don't know if this is the right place to post this or not, but I will go ahead anyway (sorry if it ain't the right place)

Yesterday I was discussing a particular theorem of geometry with my brother which he just learnt in the school. I had asked him if he knew the proof for it, he replied saying his teacher has said that wouldn't be necessary.

Then, I asked him to sit and try to prove the theorem. He said that knowing the theorem counts for more than knowing the proof. How do I explain to him that knowing the proof is more important and how it can even help expand his thinking?

I know this question doesn't have a single pointed answer as is pre-requisite for questions posted here, but I would appreciate any replies

Answer: 
An idea on why learning proofs (not just theorems) is important: One could say that it is unimportant to know how to prepare food because there is a McDonald's down the street. But, if a person becomes strictly reliant on McDonald's for preparing food, then we can be assured that (s)he will never be able to produce a (worthwhile) dish of their own creation. 

Likewise with proofs--one could say it is unimportant to know how to "prepare" the "food" of a theorem via proof because there is the "McDonalds" of the math book nearby. But, after years of just relying on memorizing theorems, a person will never be able to come up with a sound theorem of their own.

Being able to prove something makes it much more solidified in one's mind, and gives you a tool that is applicable to many circumstances, not just a single instance. For example, my double angle formula may not be useful when I need a triple angle formula, but I could use the proof/derivation of the double angle formula to *find my own* triple angle! This is where proof is much more powerful than memorization.
One approach would be to give an example of a theorem that sounds so absurd that noone in his right mind would accept it without proof. For example, mention the Banach-Tarski result to the effect that the unit ball can be decomposed into 5 parts which can then be reassembled by rigid motions into... two unit balls.

Another example would be the equality of $0.999\ldots$ to $1$. Of course, this one he won't believe even after you give him a proof :-)