How can PhD student repair relationship with supervisor after PhD student engages in independent research without supervisor?

When I had just started my PhD in Computer Science in Korea, a Physics PhD student in the EU proposed a collaboration. He and I wrote one paper for a conference. I learned last week that the paper was accepted. He is first author. I am second author.

I did not tell my professor about this project even though he was my supervisor then. I mentioned it to my professor recently. He became very angry. He asked me to remove my name from the paper. He said that all my work represents his lab and my university. I shouldn't conduct other work.

My professor's points

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  The collaboration should be done between supervisors. (My professor's background and interest do not fit with my coauthor.)

  
  


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  Another issue is none of us can present the paper at that time, asking someone for authorship is acceptable for this situation?

  
  

My question

How can I mend things with my professor and continue to collaborate with my coauthor?