Even attempting to initiate such a relationship creates problems.The subordinate may reasonably believe that rejecting the invitation will have adverse consequences at work.I suspect you are not qualified to give legal advice, and taking legal advice based upon someone's second-hand recollection of what a lawyer once told them is not a wonderful idea, either. But just "Romantic relationship which wont la(u)st long I won't recommend you to go on with such a decision.(I'm sure there is some truth to your answer, but my understanding is that the situation is a bit more complex than your answer indicates.) It's a bad idea because you cannot represent the organization's business interests properly in your role as boss, with respect to that person. To maintain your value in organization, if you still have a huge crush on her, ask her out for a date and tell her things, if you have good thoughts get her a good job in some other company using your contacts.
Every action you take regarding your romantic partner will be suspect.
How many of those relationships ended badly or turned ugly? Chances are, however you slice it, you are making a gamble and you do not have the edge. Can you please give me a [special dispensation] for this? I note that you have no citations to reputable sources, and you yourself are not a legal expert, which to me makes the answer of dubious reliability.
Given that potential scenario the companies discourage dating in the workplace to the point of making it a cause for firing an employee. (It may be accurate to say that "one of the parties can claim sexual harassment", but anyone can claim anything at any time.
A certain level of unprofessionalism will be displayed by one or both of you, which will disturb the workplace and might cause problems with your clients. Looking at the wording of your original question, I'm almost certain that you will display unprofessional behaviour and in turn cause disturbance in the workplace.
The OP is asking why it is bad between subordinates, not why it is bad at the work place. Many will perceive that the relationship is not one of mutual, personal romance.
You are likely to favor that person regardless of their performance in their job. Would you want your lower level managers supervising people who are their significant others? Then you can date her, she will like you for your gentleness.