There's a good reason that many companies do not want their employees to date. Office romances can lead to some serious complications, and it's often better just to avoid those situations entirely.
For instance, imagine that you're at work when your supervisor starts to take a romantic interest in you. The feeling is not mutual. After a while, that supervisor makes some clear advances, which you politely reject.
This puts you in a far more difficult position than if the same situation happened outside of the work environment. The Equal Employment Opportunity Commission notes that the person who makes these advances toward you could "communicate an implicit threat to adversely affect [your] job status."
Essentially, it puts extra pressure on you. If your supervisor asks you out and you want to say no, you're probably not just thinking about the personal relationship. Are you worried about losing your job? Do you worry that your supervisor will discriminate against you any time there's a chance for a promotion? Are you worried that, even if you keep your job, that person will just start giving you unfavorable tasks and negative performance reviews?
Your supervisor may not directly make that threat, but you understand the work hierarchy. You may feel trapped. You may feel pressured to allow the romantic relationship to happen to preserve your standing in the company, or you may feel like you face unwarranted discrimination simply for turning down a relationship you never wanted in the first place.
If this happens to you, it is crucial that you understand all of your rights as an employee and what you can do to combat discrimination and sexual harassment in the workplace.