How can I avoid teaching my co-worker my job?

First check to see if your job has to have a diploma attached to it and that the diploma needs a college educaiton. If it does then you can tell your boss that you can't do that because it is a job that needs a college education and you are not a lisenced teacher. Show her the proof. If it isn't that then just train her because your boss is looking out for their interests in the case that you could get sick or need emergency leave and they would have no back up person for that. My husband has that same situation so he has part time people he has trained to do his job if he goes on leave or is sick. Before that happened he got very sick and they didn't have anyone to do his job so the hospital lost money. You should not be worried about job security. What does your contract say? Also if you are that inseure about it then I would talk to your boss to make sure that your job is not in threat by you training someone. They need to know that is what you think they are thinking.