Is there a reason that jewishness comes from a mother? Now wth DNA we can know who the father is

Shalom, Thank you for your question. The fact that Jewishness runs through the mother is learnt from verses in the Torah, and is recorded as Jewish law throughout the generations. The Torah does not record the reasoning for this law, and while it is certainly acceptable (and even encouraged) to strive to understand Hashem's law, we never use any human explanations of a law to change the law itself. So, whilst it could be that part of the reason for matrilineal decent is because we can be sure of the mother, but not the father – accepting this reasoning cannot be used to change the law even if we have new ways to reach the same certainty, such as using DNA. The reason for this is that it is quite likely that any reasons we ascribe to Hashem's law are (even if correct) only partial answers. There are so many more reasons, and certainly on a spiritual level, so many more answers that we as humans cannot possibly attain, that we can never assume that we have grasped "THE REASON" for any law. With this being so we delve into every law, and get great benefit from seeing different reasons for each and every detail – but we never let those understandings become more important than the law itself. With this law we can understand that the reason Judaism follows the mother is not just a question of identification. There are certain social, psychological and spiritual forces that come through the mother that apparently play a big part in determining the status of the soul. I hope this short explanation of a big topic is of some help to you. Blessings.