It is not permissible for one who has started an obligatory fast to break it without a legitimate shar’i reason

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? 

He replied: 

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.