Breeding *is* genetic engineering.
The difference between laboratory engineering and engineering via other methods is that in the lab, a degree of precision is possible that cannot be achieved by any other method.
I can literally change one single base pair of DNA and leave the entire rest of the genome untouched when using lab methods of genetic engineering. On the other hand, if I try to breed animals or plants for a trait, I may or may not get the trait... the trait could be linked to another trait that I do not want at all... there are unpredictable changes to the rest of the genome that can affect the organism's growth, appearance, health, flavor, etc.
The difference between older methods of genetic engineering and laboratory methods is analogous to the method of painting a wall in your house by throwing random cans of paint at it and hoping for the right color and complete coverage, vs. getting a can of paint of the desired color and applying to the wall exactly where you want it with brushes and rollers.