Question

Hello Rabbi,

There is a not-so-clear Talmudic passage in tractate Shabbat 12a:

The Rabbis taught: One may not inspect clothing for lice in the public domain, out of respect for human dignity. Similarly, Rav Yehuda—and some say Rabbi Nehemiah—said: One may not induce vomiting in the public domain, out of respect for human dignity. The Rabbis taught: One who picks lice from his garments may crush them and throw them away, provided that he does not kill them. Abba Shaul says: He may remove them and throw them away, provided that he does not crush them. Rav Huna said: The Jewish law follows the view that he may crush them and throw them away, and this is respectful behavior, even on a weekday. Rabbah would kill them, and Rav Sheshet would kill them, and Rava would throw them into a basin of water. Rav Nachman said to his daughters: Kill them, and let me hear the sound of those who hate me.

It seems that the Talmud means that the prohibition against killing the louse is because of human dignity, not because of the Sabbath. But then it is hard to understand why the Talmud says the words "even on a weekday." Is there a difference in human dignity between a weekday and the Sabbath?
Best regards,