Steve Hynd distills one of the strongest anti-intervention arguments to its core:

[Responsibility] to Protect interventionism is essentially a utilitarian argument - that by using violence in reply to violence the greater good of the greater number can be achieved - specifically, that fewer people will die if there is an armed intervention than if the state or non-state actor is allowed to continue killing unopposed by external forces. But it largely ignores a wider utilitarian argument to do so - that the resources required to intervene could be put to better use saving more lives elsewhere...I doubt the dead care whether they are killed by a bullet or starvation - they're still just as dead. Utillitarian ethics, such as those used to justify R2P interventionism, dictate that resources should first go to missions which would help the greatest number - yet the budget for Somalian aid is a measly $105 million.

Previous discussion of this line of argument here. I can think of fourth responses at the moment. First, one could make non-consequentialist arguments justifying intervention based on the particular moral heinousness of mass slaughter as compared to other lethal ills. I'm not compelled by the underlying moral reasoning here, but I could see how one might be. Second, one could say it's an argument for more aid AND intervention. That'd be fair enough, except for the fact that states do lots of things to save lives other than aid and intervention that draw from the same finite resource/tax base. So that argument might work depending on the resource constraints at play, but it also might not. Third, an intervention might be politically possible whereas aid increases might not. Again, that might be true in a given case, but it doesn't answer Hynd's more fundamental moral challenge.

There's a fourth, though, that's more compelling: humanitarian intervention is often necessary to create the conditions under which aid can be effective in saving lives.