Why is it impossible to find the private key from the public key? From what I understand, based on the article A Beginner’s Guide: Private and Public Key Cryptography Deciphered, the public key is generated by performing $n$ tangent plus mirroring operations from the point $G$ over the elliptic curve, where $G$ is defined in secp256k1 and $n$ is a natural number that directly relates to the private key. 

As I know the public key and the seed value $G$, I could start a process computing $$G + G, G + G + G, \dots$$ and comparing those results with the public key value until it matches. 

If your answer would be that this process is very slow: if this process is slow, the same applies to computing the public key from the private key (because the operations are the same except for the check operation). So, how it is possible to compute the public key in a very fast way?
My question is: as I know the public key and the seed value `G', I
  could start a process computing G + G, G + G + G, and comparing those
  results with the public key value until it matches.


You can, but you have to check about 2256 values. This is an extremely big number. So it is computationally infeasible to perform this operation. 


  If this process is slow, the same applies to, knowing the private key,
  and compute the public key (Because the operations are the same except
  for the check operation), so how it is possible to compute the public
  key in a very fast way?


Because we compute public key in smarter way. You are trying to check all values by continuously do + operation. But to generate public key we use * operation: public = private * G