Why is it impossible to find the private key from the public key?
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