Saying that I'm a lesbian has never made it any easier to disengage from an amorous man in an "I am not going to leave you alone" situation. Sometimes it makes the situation worse. I finally learned and don't do it any more.
I live in Seattle which is fairly gay friendly so I've never been very scared that any homophobes are going to kill me or anything if the subject comes up (or if they try to kill me someone will stop them).
The "amorous man" situation usually applies to when men try and kind of pick me up when I'm walking along in the street, and they start to follow me and my polite yet firm "I'm not interested" has been ignored. When I was younger and more foolish I somehow thought lesbianism was the ultimate get out of jail free card when it comes to amorous men. This got me reactions like:
-That's fine babe I like lesbians.
-Cool! I've never done it with a lesbian!
-Suck my cock lesbian bitch I'm calling the police and you'll see how they deal with dykes.(I'm not sure what this guy was thinking, or how he thought the police could help him. He wasn't interested in romancing me any more, which was good, BUT he kept following me and screaming for a block)
-So you have a girlfriend. Don't you need a boyfriend to?
-Oh good. So you DON'T have a boyfriend!
I finally finally realized that if the guy ignores my request that I be left alone then I can yell profanities at him and that's the only thing that works quickly, and leaves me feeling self satisfied and I like I have some control over the situation.