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.
I'm sure I could write more about why proofs are important, but I believe it all boils down to this. Proofs are important because some very intuitive results turn out to be false, and if we just accept results with no proof because something 'sounds correct', then we could be led down false pathways. Who knows what horrors that could reap?