In reply to Anders Møller Greve.

Yes, it can be confusing because there are so many symmetries. For example, do you model the event as X=1 or as X=0? Are you interested in the ratio P(Y|X=0)/P(Y|X=1) or the inverse ratio? In practice, we are guided by domains-specific knowledge such as assuming that the experimental treatment will have a certain effect compared to the control group. That domain knowledge helps you to write down the null and alternative hypotheses.