Why don't teachers just tell us the answers?

Because, human can only gain WISDOM by tackling problems, having experience and getting answers afterwards.

Getting answers is useless for many questions without having experience.

Tell me a single teacher who is teaching without being a student.

Because it is so difficult to answer these questions in a straightforward manner with only a sentence or two.

The best way to answer the specific question would be to not answer it at all, but since this site is about instant information, I will go on.

If you get the information from someone or something outside of yourself, you only get the data, if you ponder it in your own mind, you gain insight and the answer is truly yours.

Koans are specific instruments to help you learn, not just receive information.

Actually the teacher has already told us the answer, but due delusions and obscurations, we cannot see the answer. Just like if there are clouds, one can never see the sky.

Answers are written in plain language in plain sight in books you can buy anywhere and may already own. Sometimes we miss the underlying sense of a sentence because the subtlety is hard to grasp. But no one is hiding anything from you.

What began to make me personally understand a lot more was thinking about the five skandhas after reading D.T. Suzuki's Manual of Zen Buddhism.

And funnily enough, the first time I experienced an 'aha!' moment was looking at a tree outside while listening to the Gospel of John. Notice how both Jesus and Buddha talk about seeds?

Now a good report of Master Gotama has been spread to this effect: 'That Blessed One is such since he is arahant and fully self enlightened, perfect in true knowledge and conduct, sublime, knower of worlds, incomparable teacher of men to be tamed, teacher of gods and humans, enlightened, blessed. He describes this world with its gods, its Maras, and its (Brahma) Divinities, this generation with its monks and brahmans, with its kings and its people, which he has himself realized through direct knowledge. He teaches a Dhamma that is good in the beginning, good in the middle and good in the end with (the right) meaning and phrasing, he affirms a holy life that is utterly perfect and pure.

Is the stock description of 'the' Buddha. It has terms that likely need to be further defined - fully self enlightened, Dhamma - that will likely have even more terms that need to be defined, but overall the above should do the trick. 'What is Buddha' asks a question looking for something closer to Essence imo, and that's not really within the Dhamma.

"What is your original face" I am not sure about! Reading about it a little, if it hints towards dependent origination, then it's an insight into the fact that 'I hit you with a stick' is mirrored by 'You are hit with a stick, by me'. Subject depends on object and object depends on subject - there is no event that can be described within the world that is not subject to this. If it is to do with some notion of an eternal self when the mind is fully stilled, it is again not part of the Dhamma, as it is wrong view, Brahmajala Sutta for 'eternal', Mulapariyaya Sutta for 'Self'. The experience of Nibbana - the end of mental fabrications - is unconditioned, so 'original', 'eternal' or even 'self' would not be accurate.

Because the mind is like the stream, the width of it dictated the water capacity. Normal mind runs on intellect, a PhD, or common genius mind like certain mathematician scoring IQ 200 is just that the current of the stream is swifer, not the capacity enhanced. With Koan the Huatou the mind is stuck for the questions are crazy, nonsensical. Working on it rigoriously but trapped, forced the mind evetually breaks through the intellect confinement thus really "upgraded", realized the beyond the frontier veiled by the five senses and intellect-Mind. Like the water breaks up the bank and flooding. Hence when the great master of ancient enlightened, none of them wrote down a correct answer to any Huatou, instead, most wrote poems (and a true teacher was able to see if the student really arrived by reading the poem) which are none to do with the question. So don't be fooled by the questions ;) thinking they must be so sophisticated, no. But yes, also, they have the power to trap/engulf a brilliant mind.

These have a lot to do with the "magic" the Chinese this unique language. I really doubt the same favour could be preserved when working with other language. Japanese is kind of exceptional because in ancient time until Song Dynasty of China, Japan, Korea was adopting Chinese. Thus their tradition of Ch'an Koan was a Chinese language version. Language, an accomplished teacher who knew where the student reached, is the key. I doubt nowadays where these could be found.