What does he mean by "my place"? Does he mean it's not his business or it's something he shouldn't interfere?

Native speaker’s answer
Rebecca
Yes, you've got it! If something isn't someone's "place", it means they're not in the position to say or do anything and that they shouldn't interfere- as you said. Ex: Jim, it is not your place to contact clients directly. If you have an issue, please come to me first. Ex: It's probably not my place, but I think Liz is right.