Answer:
Because they were able to create a widely-used operation that could lead them to being famous or gaining some recognition as doctors.
Explanation:
So Dr. Nemur states that it's his experiment, therefore he should handle it however he pleases, but Dr. Strauss claims that he contributed just as much, therefore he should get credit as well. Because of this, Dr. Struss mentions that their brilliant operation is being used world-wide, which could be big for them for many reasons. So, they're fighting because it's a potentially big thing that could grant them some recognition ad doctors.