[I thought about that question as it became even more relevant with the advent of cooking TV shows where a Jew might be involved in cooking non-kosher foods with no intent to eat it or serve it to Jews.]

I see two major and two minor issues which, practically, would make participation in a cooking school complicated (there might be more - would love to get feedback).

 1. the prohibition to cook (and not just eat) a mixture of meat (from a kosher animal) and milk
 2. [marit ayin][1], giving the appearance of doing wrong
 3. an additional issue on Pesach since a Jew is forbidden to own hametz - so any hametz he would be given to cook would be problematic
 4. similarly *orlah* fruit in Israel would be a concern (see [here][2] on 3 and 4)


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**1. Milk and meat**: it is forbidden to cook meat from a kosher animal with milk (see MT [Hilchos Maacholot Asurot 9:1][3] and further sources [here][4]).

There might be ways to circumvent these prohibitions, e.g., cook only poultry or meat from non-kosher animals, or cook in non-kosher milk. Alternatively [ohr.edu][5] suggests a non-Jew could light the fire while a Jew cooks.

Interestingly, Rav Moshe Soloveitchik ruled that one may cook meat and milk together for a scientific experiment in which there is clearly no intention to eat the mixture (see Rabbi Hershel Schachter's "Peninei Ha-Rav," p. 152, quoted [here][6]). A rav would have to be consulted to see if one can extend it to cooking in a school since there is a benefit as well (learning to cook) but no intention to eat.


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***2. Marit ayin*** prevents a Jew from doing anything that gives the appearance of transgressing the law, even if he technically doesn't. A relevant example here is eating meat in almond milk.

R David Brofsky [writes][6] there is a *machloket poskim* (rabbinical dispute) whether marit ayin applies in such a case. The Rashba (Teshuvot 3:257), and later the Rema (YD 87:4) rule that a priori one should not cook a non-kosher animal in milk because of mar'it ayin.  The Shakh and Taz both challenge this ruling.

For a Jew to cook in a cooking school, he would have to explain all the precautions he is taking not to transgress halacha, incl. the fact he wouldn't eat the food or serve it to Jews.

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As always, [speak to your rav][7] before attempting anything you have read about on the Internet.


  [1]: https://judaism.stackexchange.com/questions/7459/what-is-maris-ayin
  [2]: http://www.crcweb.org/kosher_articles/benefitting_from_non_kosher.php
  [3]: https://www.sefaria.org/Mishneh_Torah,_Forbidden_Foods.9.1?lang=bi&with=all&lang2=en
  [4]: http://dinonline.org/2017/11/02/basar-bchalav-question/
  [5]: https://ohr.edu/ask_db/ask_main.php/112/Q1/
  [6]: https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwjEjsS03tHXAhXKD8AKHbGJDDsQFggtMAE&url=http%3A%2F%2Fetzion.org.il%2Fen%2Fdownload%2Ffile%2Ffid%2F4096&usg=AOvVaw0HgmyFJ8M9RXEpiIsRtpoZ
  [7]: http://judaism.stackexchange.com/q/9146