Consider this argument against determinism: Determinism requires that all future facts follow from the laws and the present state. But the laws of nature make no reference to particular individuals or to haecceities. Thus, the laws underdetermine which particular individuals will come into existence in the future. The laws can only determine what these individuals will be like, cannot determine their numerical identities.
We could use modus tollens on this kind of argument. It is possible that determinism holds and yet individuals come into existence. Therefore, the identity of individuals must be determined by their causal history, if determinism holds. But the only plausible reason to think that the identity of individuals could ever be determined by their causal history is if we think that, in an appropriate sense, identity is constituted by causal history.