It is true that in my US universities there is a blanket rule about it, which is an overkill. What is not "kosher" is the use of power in the context of a sexual relationship. So a professor should not be in a relationship with her current student. This is so for two reasons:

- the professor has power over the student and hence can abuse the power to extract sexual favors from the otherwise unwilling student; that is abuse of power and that is clearly very bad

- the professor can inflate the student's grade beyond what is earned in reality (this is an issue in the context of gradable essays - with computerized multiple choice tests, it is a non-issue) and that is unfair to the classmates of the student in question.

Both abuse of power and unfairness are bad things, so those are valid reasons to prohibit a relationship. Beyond that, it is just fear of liability. So it is quite possible that where you are you can have a relationship with her AFTER you complete the coursework.

I met with my former colleague who is now dating a guy from her team, in a large tech company. They disclosed the dating relationship to the management and were asked not to write each other's performance reviews. That is a reasonable approach. They can stay on one team (she enjoys working with him around) provided they do not try to inflate each other's performance scores via writing positive reviews.

In law firms, a partner who dates an associate does not contribute his/her opinion in the review if the associate is considered for a partner. Same reasoning - fairness/abuse of power.