According to historian Shaye J. D. Cohen, the status of the offspring of mixed marriages was determined patrilineally in the Bible. He brings two likely explanations for the change in Mishnaic times: first, the Mishnah may have been applying the same logic to mixed marriages as it had applied to other mixtures (Kil'ayim). Thus, a mixed marriage is forbidden as is the union of a horse and a donkey, and in both unions the offspring are judged matrilineally. Second, the Tannaim may have been influenced by Roman law, which dictated that when a parent could not contract a legal marriage, offspring would follow the mother.
Try to answer this question if possible (otherwise reply "unanswerable"): What dictated that when a parent could not contract a legal marriage, offspring would follow the father?
unanswerable