Why would existence remove my knowledge after reicarnation? Avidyā and moha which can be translated as confusion or ignorance are sources of suffering. The western term for the study of reality and knowledge is called "philosophy" which an be translated from the Greek as "the love of wisdom". 
Rāga is also a term for attachment which is another source of suffering that is to say Buddhism tells you not to attach yourself to material or mental objects (including Buddhism) otherwise you will suffer and won't attain enlightenment.

If knowledge gives you a deeper understanding of reality and existence and makes you understand other beings and their need to escape suffering and knowledge makes you attain compassion, why would nature be so cruel to remove your memories and wisdom reincarnation after reincarnation to make you step on the same stones again? Christian Gnostics believed that it's because this world is controlled by Satan and only holy knowledge can give you salvation. Is karma (which is a religious belief) the only answer Buddhism has to this matter?
why would nature be so cruel

"Cruel" sounds like dukkha -- as if nature were ill-willed and unkind, and we were averse to that.

So I guess that's among the many kinds of view or perception that we should overcome (in order to do away with dukkha), craving things to be other than they are -- though maybe also acknowledge whatever truth there is in it to become dispassionate about whatever is impermanent.


  "He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.


to remove your memories and wisdom reincarnation

I suppose you're not supposed to see them as "your" memories and "your" wisdom.

They are memories, perhaps they are wisdom, but they are, "not mine, not me, not my self".

To some extent wisdom isn't removed -- from the world -- by death, in that the Dhamma continues to exist. I think that's similar to the view that there's a dharmakaya.