Sentence 1 does not have any generally understood meaning. If you change 'with' to 'by', it means the same as 2.

Hello! The phrase that I would use to express what you want to say with your example is: 2. I don't like being on my own. I prefer being with other people. That doesn't mean that the expression "with myself" doesn't exist or is wrong, it's just used a bit differently. For example: "I'm happy with myself." means you are happy with who you are. "I'm struggling with myself." means you are having inner problems or dilemmas, with your own thoughts, feelings, etc. In fact, if you were to say the first part of the first sentence you proposed: 1. I don't like being with myself. It would mean something more along the lines of "I don't like myself". It wouldn't mean "being alone" as your intention was, if I guessed correctly. If you wanted to use an expression to say "alone" that used the word "myself", you could say: "I don't like being by myself." This would be the equivalent of saying "I don't like being on my own." or "I don't like being alone."

They have identical meanings in your example sentences. To be on your own could also mean to be single/unmarried. In this sense you would not describe the person as being with himself/herself.

1. I don't like being with myself. I prefer being with other people. This isn't quite right. It should be 'I don't like being BY myself'. 2. I don't like being on my own. I prefer being with other people. This is fine. If you make the correction to the first sentence, the two sentences have the same meaning.

With regards, In many cases, they are interchangeable. However, there is a subtle difference. "On my own" is used more for doing something with no help, where you would usually expect help - also when making a decision when it might be expected that you would try to get somebody's permission or agreement. From my points of view, the first sentence makes more sense. Regards.