That first sentence isn't quite right. I agree, personally, that every political system should be burned to the ground but, as usual, some Marx might give a slightly saner perspective here: the problem is precisely that there
is a political system, which separates political personhood from private, civil personhood. Today, a group of people acts in social cooperation primarily through a political system. They may have an important social goal, like improving child nutrition, but the political system has already leeched the social power necessary for its achievement. Thus, any other social goals being worked out through the political system, such as economic growth, national security, even personal liberty, are at odds with the social goal you're concerned with, simply by nature of having to work through a defined, singular system. You can only push and pull a lever in so many directions, no matter how complicated and multi-axial it is. And as a sidenote, the political system itself doesn't have goals, even if its initial creation did have specific goals. They inform the system, but are not properties of it.
The intent of communism (esp. with the abolition of the state) is not, contrary to many views, some evil dictatorial master plan, but simply to put social power back into the hands of the people, allowing the existence and implementation of real social priorities, such as child nutrition.