Two of the big claims against International Law, well, actually three, go at the very heart of International Law, one, if international law, can be understood as seen as really international, and on the other side, if it can be referred as, well, law. However, another aspect that lies behind those two claims, is to understand if international law is or can be seen as science.
In the first aspect, as to the internationality or not of international law, lies this tension between eurocentrism, and New Approaches to International Law, and with it Third World Approaches to International Law. What is the level of internationality to claim something is really international? Awareness, active participation or acquiescence? What is the degree?
On the concept of law, should international law be worried (as being a subject) at all, should be international law be examined under the municipal law standards as to their respective characteristics, centralized government, or not? One legislature and of course one court to govern us all.
As to being a science, well, it is not, if you refer to it as an exact science.
And, should will be worried at all that maybe is not as international as one might think, or as a hard law as one must expect or a science to one surely wants it to be?
No. But that does not mean that we should stop being rigorous as to what we are studying, which is International Law.