I don't see where gender inequality comes into the picture. According to me, it is simply a polite way to address people, especially if it is in a formal setting. It may be considered very rude to say "Hello everyone" if, for example, you are addressing the CEOs of top business houses. You do have to keep the context in mind. I think it would be OK to say "Hello everyone" if it was an informal setting, such as a group of colleagues or at a party or even, say, at a fine dining restaurant where there is an informal atmosphere and you are called upon to give an impromptu speech as part of some fun activity.
Keep smiling...one day life will get tired of upsetting you.