Kratos has pride over being a Spartan and still is a living representative of Spartan culture and ideals. So, why does he not want Atreus to be trained or treated like one?

Kratos is a proud Spartan. He loved his birthplace and no doubt that it was thanks to his Spartan training that he was able to become a successful general of Sparta. So why is he so against Atreus being trained like one? Not only is he against being treated like one, he is against Atreus acting like one. I know that Spartan training is rigorous and cruel and that he probably feels that it was way too harsh and punishing and that Atreus did not have to train like one, yet Kratos still upholds these ideals in the way he thinks and acts. He is a Spartan through and through. Does Kratos have a sort of shame in some of Sparta's traditions and does he feel the need to change because of it? Or does he still embody these ideals because it was hardwired into him as a child?