Have you a concrete idea how what private services you would use to prevent animal cruelty?
If you have to ask this, you're not getting the point of "personal responsibility". YOU are the private service that prevents animal cruelty. Any questions?
If we take such a position as a starting point, couldn't we come to what we already have there, i.e. state? I mean that we delegate some functions to someone or to some entity, and thus we are laying a basis for building a hierarchy here. Isn't it what state is all about and could there be such functions which are best served when they are at the top of the hierarchy ("the only true provider")?