Most of the time, they shouldn't even ask for a reason. If they do, you always just say it is an immigration matter and its confidential to you. There isn't a major reason to lie, but if it comes down to it, you could always say you changed your SSN because you felt insecure with your current SSN. Also reminding your employer that you are allowed to change your SSN up to 3 times in your lifetime. So what you are doing is not illegal or against the law.