Praise be to Allah.
It is not permissible for a man to be alone with a woman or teenage girl who is desirable, whether that is for a private lesson or anything else, in the home or elsewhere, because the Prophet (peace and blessings of Allaah be upon him) said: “No man is alone with a woman but the shaytaan is the third one present.” Narrated by al-Tirmidhi (2165); classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
And he (peace and blessings of Allaah be upon him) said: “No man should be alone with a woman unless her mahram is present.” Narrated by al-Bukhaari (3006) and Muslim (1341).
What is meant by “being alone” is their being in a place where no one else can see them.
The stories which one hears about male teachers and female students are very disgraceful, and mean that the girl’s guardian must be even more careful and cautious.
The reason for that – and Allaah knows best – is that the girl is usually young, at the stage of adolescence, when desire is strong, and it is easy to deceive her, and she does not have enough common sense or experience to be able to understand things properly and control her desires. Moreover, lengthy interaction between the teacher and student, if it goes on for a year or more, will gradually reduce the shyness and modesty between them, which will make it easier to fall into that which Allaah has forbidden.
The one who finds that he needs to bring a teacher for his daughter must make sure that someone sits with them during the lesson, such as her brother, or he should make sure that the lesson is given in an open area of the house, such as the sitting room, for example, and not in a closed room.