Praise be to Allah.
If a person starts to observe an obligatory fast, it is haraam for him to break it without any reason. If he breaks it he has to make up this day. Ibn Muflih said in al-Furoo’:
It is haraam to break an obligatory fast.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked in Fataawa al-Sawm (p. 452) about a woman who was making up a missed fast, then some guests arrived at her house and in order to join them she broke her fast – is that permissible?
If she was making up a missed obligatory fast, such as making up missed days from Ramadaan, then it is not permissible for anyone to break such a fast except in cases of necessity. With regard to breaking the fast because of the arrival of guests, this is haraam and is not permissible, because the basic principle of sharee’ah is that anyone who starts an obligatory action must complete it, unless he has a legitimate shar’i excuse (for not doing so).
But if he is making up a naafil fast, then he does not have to complete it, because it is not obligatory.
He also said in Fataawa al-Siyaam (p. 451):
If a person starts an obligatory fast, such as making up a day missed in Ramadaan or kafaarat yameen (expiation for breaking a vow) or expiation for shaving during Hajj – if the pilgrim shaved his head before exiting ihraam – and other kinds of obligatory fasts, it is not permissible for him to break it except for a legitimate shar’i reason. The same applies if he starts any obligatory action – he is obliged to complete it and it is not permissible for him to stop it except for a legitimate shar’i reason that allows him to do so.