Other prohibitions that the hachamim (the Sages) instituted in order to prevent a person from violating having relations with a woman he's not supposed to be. The Mishnah says that one should not be a schoolteacher for children. That type of job would bring him into contact with the mothers of those children, and it could end up becoming a problem when mothers bring their children to him. An unmarried man who has certain desires and has been in contact with these women too often could have a problem develop between them. A woman is not allowed to be a schoolteacher for young children either. We're nervous here that she's going to be alone with the fathers who are bringing the children to her, and it's going to lead to a problem between them.
What we are saying here is that, when it comes to the male schoolteacher, the problem is not yichud (seclusion); the problem is hergel. They're going to be around each other too much, and there's going to be a relationship built between them. That is why, if he is married and has less desire because he has pat b'salo, his desire is already taken care of because of the fact that he's with his wife, and that mitigates the issue. So it's not a yichud issue; it's more of a hergel issue, because they'll be constantly with each other.
When it comes to the woman, even if she's married, it seems to me there's a problem because of yichud. The Bach answers the question. He says that a woman usually taught in the house of the children, and therefore she may be alone with the father in the house. As opposed to the male teacher, who teaches in the yeshiva, in the school, at that point in time there are other people around, and there's no yichud issue.
Rabbi Eliezer is going to be more machmir (stringent). Rabbi Eliezer says: Not only is somebody who is single not allowed to teach children, but even somebody who is married should not be a schoolteacher if his wife is not with him in the school building at that moment, because of the hergel: he'll be around the mothers of those children that he teaches often, and it could lead to a problem even if he's already married but is not actually with his wife at that moment.