Học = learn or study; but "I study cooking" (as in the subject) is rejected here.
Học = in Vietnamese can be used as in learning and studying.
But it's incorrect in English to use them interchangeably. Because studying is specific to school stuff. Where you use your brain. Where learning, is more practical, hand-on stuff
Not in english. Which is the problem here. I can study cooking. There are school specifically for that. So in english it can still translate to study
How do you learn but by studying? Semantics and the course does not provide differentiation rules for some words with multiple meanings and many simple sentences provide no context.
There is no differentiation in the translation, so both should be accepted. The difference in English between studying and learning is partly that you learn when/while/if you study, whereas in Vietnamese the differentiation either isn't there or it exists in the context of the bigger conversation. But the point is, plenty of people do study cooking and culinary arts, from books and in schools. This question/answer are flawed to be sure.