Perhaps it's not liberal/conservative or Democrat /Republican. Perhaps the divide is in the concept are human animals ment to be cooperative/sharing and tribal, or lone/ selfish independent hunter types.
While I think your point is in the right direction I see the difference (at least in contemporary America) as more of a question of shared benefits AND shared costs or individual benefits and shared costs. The increase in privatization of social services means that companies and individuals can now profit at a greater level for public benefits so owners are, in a sense, double dipping in benefits while the greater public sees a double helping of costs in everything from higher taxes to environmental damage done by deregulated private industry.
If it were just individual vs group good arguments could made in favor of both sides but when costs and benefits aren't distributed equitably the value of opposing arguments changes.