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Is it forbidden to cook meat and milk if one wasn't to benefit from it? The situation is being a culinary class in a non-Jewish school - would I not be able to participate in cooking if there was meat and milk?
If I could, would it be permitted to give that food to a non-Jewish teacher, explaining that I can't eat the food?
It is forbidden to cook kosher meat and kosher milk even if not benefitting from it as the Rambam writes in Ma'achalot Assurot 9:1-2. The Shulchan Aruch (YD 87:3) permits cooking and benefiting from meat from a non-kosher animal cooked in milk. As such it would also be permitted to give it to a non-Jewish teacher.
However, you would need to deal with marit ayin, the prohibition of appearing to do forbidden activities. And since it is very likely a student in a cooking class would be confronted with obviously non-kosher food (e.g., forbidden meat or seafood), it is likely to be very tricky.
See more issues and sources in a related answer here.
Of course, consult your rabbi before implementing anything you learn here.
If a person argues that Avram prepared Milk & Beef (חָלָב וּבֶן־הַבָּקָר) for angels to eat in [Bereshit 18:8]. Another could argue Avram did not command Milk & Beef to be cooked together, yet the angels [Yoklu יאכלו] still "ate" both provisions when Avram served them in Bereshit 18:8.
And he [Avram] took cream and milk and the calf that he had prepared, and he placed [them] before them, and he was standing over them under the tree, and they ate. (וַיִּקַּ֨ח חֶמְאָ֜ה וְחָלָ֗ב וּבֶן־הַבָּקָר֙ אֲשֶׁ֣ר עָשָׂ֔ה וַיִּתֵּ֖ן לִפְנֵיהֶ֑ם וְהֽוּא־עֹמֵ֧ד עֲלֵיהֶ֛ם תַּ֥חַת הָעֵ֖ץ וַיֹּאכֵֽלוּ)
Then why not offer a greater discussion about enjoyment/benefit of cruel actions - prohibited in [Shemot 23:19] לֹא־תְבַשֵּׁל גְּדִי בַּֽחֲלֵב אִמּֽוֹ ; [Devarim 14:21] - as one abstains from cooking animals in the nutrition which should have been used to sustain their life like consuming a stillborn.
Ramban states : "one forbids deriving benefit from it, and one forbids cooking it." [Commentary on Devarim 14:21; https://www.sefaria.org/Deuteronomy.14.21?with=Ramban&lang=bi&aliyot=0]
Rabbeinu Bahya claimed - "the prohibition to derive indirect benefit from the result of boiling milk and meat together" based on (Chullin 115b.4; https://www.sefaria.org/Chullin.115b.4?with=all&lang=bi).
Serving discussions about animal cruelty [Shemot 23:19, Devarim 14:21] instead of cooking milk with meat might not bring joy to our stomach, but will fill our heart with compassion.
