Kratos is not entirely cold and unfeeling, although he puts across that message. I really don't want to go all analysis on anyone, but I do have plenty of evidence to back myself up on that point. He does appear cold at times, yes, but he has his reasons and they aren't that he's only concerned with himself and doesn't care for anyone else.

We have to think that in game, Kratos is over 4000 years old. He is no longer human. He will outlive anybody he speaks to, and the last person to attempt to persuade him that he was human where it mattered died at his hands. He can't allow himself to get close to any of the regeneration group because in the end, Colette will die, the others will grieve for her, he will have caused it and he will be leaving when Colette does anyway.

His distance is an attempt at damage limitation, both to the group and to himself. He doesn't want to become something to be missed alongside Colette and at the same time, he can't afford to feel too deeply for these people he will have to betray and leave behind (which, of course, fails the moment Lloyd comes along).

When we then think that he ends up doing things like offering to help teach Genis the Angelic language alongside Colette, although it would be more beneficial to him to leave it to the Chosen and not reveal his knowledge, it gets even greyer. He had no need to do that. Certainly, it doesn't benefit him in any way, aside from making Genis like him more - and it doesn't matter if they like him as long as they need his paid sword to keep Colette safe - that's all he really has to do.

So he's not the cold-hearted killer he appears to be.

Of course, he's distanced. Perhaps even a little awkward in the way that he socialises. It takes a lot for Kratos to let a person in. But when he does, he cares for them very deeply. He just doesn't often show it, on account of the fact that he himself feels estranged from the world and that any kind of relationship with him can only be damaging.

Damaging because Kratos carries the weight of 4000 years of guilt he can't let go of (both of things he was and was not actually responsible for). Having added to it for so long, he genuinely believes he isn't really deserving of affection - and also that he is more dangerous than he really is.

His fears aren't entirely groundless. He has to appear as an enemy to his son for a large part of the game in order to save him in the end. His aim is to die an enemy. His being friendly with his son before his death would only serve to upset Lloyd - particularly since Kratos would effectively die at his hands. If he is an enemy, it allows him to guide Lloyd's growth and test it in that duel, without causing Lloyd any grief in the process.

Again, this fails the moment he's outed at Altessa's House. But that way of thinking still stands. That the best way of avoiding the pain of others (and adding to his own) is by not engaging them.

Kratos blames himself for Mithos' mistakes. He feels he hurt and made Yuan ashamed. He allowed Martel to die, killed Anna with his own blade and he lost Lloyd and failed to find him. These are his closest people and he feels he is to blame for a lot of their failings and sufferings. Letting people in means putting them at risk of that fate, and himself at risk of having to witness that loss again, although he only thinks in terms of not harming anybody else.

This isn't the avoidance of someone who doesn't want to deal with the world. It's the motion of a man who has seen too much loss from it. He denies physical emotions so that others think him stronger than he is,  they don't worry about him and nobody understands his true feelings or attempts to approach him on account of them.

It is safer for a man who has truths to hide to have hidden away any clues to them. It's also easier for somebody who has lost everything to put on a face that shows nothing.

As I've put before, Kratos wasn't always as he is now. I think pre-Kharlan Hero Kratos was more open, more like Lloyd in the way he held ideals and was determined to do what he could. The Kratos we see in game is derived from the mask he had to wear as he climbed the military ranks, the years and certain events having whittled away what was initally underneath it.

But that doesn't mean nothing is underneath it. Just that what is underneath is weighed down by the four-thousand years of life and mistakes he never ought to have had.