Why does it seem false?

If welfare of strangers is something you value, then it is not a net cost.

Yes, there is an old-fashioned definition of altruism that assumes the action must be non-self-serving, but this doesn't match common contemporary usage (terms like effective altruism and reciprocal altruism would be meaningless), doesn't match your usage, and is based on a gross misunderstanding of how morality comes about (if written about this misunderstanding here - see section 4, "Honesty as meta-virtue," for the most relevant part).

Under that old, confused definition, yes, altruism can not be rational (but not orthogonal to rationality - we could still try to measure how irrational any given altruistic act is, each act still sits somewhere on the scale of rationality).

It does not.

You seem very confident of that. Utterly bizarre, though, that you claim that not infringing on people's rights is not part of being nice to people.

But the social contract demands much more than just not infringing on people's rights. (By the way, where do those right come from?) We must actively seek each other out, trade (even if it's only trade in ideas, like now), and cooperate (this discussion wouldn't be possible without certain adopted codes of conduct ).

The social contract enables specialization in society, and therefore complex technology. This works through our ability to make and maintain agreements and cooperation. If you know how to make screws, and I want screws, the social contract enables you to convincingly promise to hand over screws if I give you some special bits of paper. If I don't trust you for some reason, then the agreement breaks down. You lose income, I lose the screws I need for my factory employing 500 people, we all go bust. Your knowledge of how to make screws and my expertise in making screw drivers now counts for nothing, and everybody is screwed.

We help maintain trust by being nice to each other outside our direct trading. Furthermore, by being nice to people in trouble who we have never before met, we enhance a culture of trust that people in trouble will be helped out. We therefore increase the chances that people will help us out next time we end up in the shit. Much more importantly, we reduce a major source of people's fears. Social cohesion goes up, cooperation increases, and people are more free to take risks in new technologies and / or economic ventures: society gets better, and we derive personal benefit from that.

I think we have a pretty major disagreement about that :-/

The social contract is a technology that entangles the values of different people (there are biological mechanisms that do that as well). Generally, my life is better when the lives of people around me are better. If your screw factory goes bust, then I'm negatively affected. If my neighbour lives in terror, then who knows what he might do out of fear - I am at risk. If everybody was scared about where their next meal was coming from, then I would never leave the house for fear that what food I have would be stolen in my absence - economics collapses. Because we have this entangled utility function, what's bad for others is bad for me (in expectation), and what's bad for me is bad for everybody else. For the most part, then, any self defeating behaviour (e.g. irrational attempts to be nice to others) is bad for society, and, in the long run, doesn't help anybody.

I hope this helps.