He fasts one day and not the next, what are the days when it is forbidden to fast?

Praise be to Allah.

We ask Allaah to help you, and to accept your fasting. 

Concerning the virtue of the fast of Dawood (peace be upon him), al-Bukhaari (1079) and Muslim (1159) narrated from ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “The dearest of prayer to Allaah is the prayer of Dawood (peace be upon him) and the dearest of fasting to Allaah is the fast of Dawood. He used to sleep half the night, pray one-third of it, and sleep one-sixth of it, and he used to fast one day and not the next (i.e., fast alternate days).” 

With regard to the days on which it is not permissible for you to fast, they are the day of Eid al-Fitr, the day of al-Adha and the days of Tashreeq which are the three days after the day of al-Adha. 

That is because of the hadeeth narrated by al-Bukhaari (1889) and Muslim (1920) from ‘Ubayd the freed slave of Ibn Azhar who said: “I witnessed Eid with ‘Umar ibn al-Khattaab (may Allaah be pleased with him) and he said, ‘These are two days which the Messenger of Allaah (peace and blessings of Allaah be upon him) forbade us to fast: the day when you break your fast and the other day when you eat of your sacrifices.’” 

And al-Bukhaari (1884) narrated that ‘Aa’ishah and Ibn ‘Umar (may Allaah be pleased with them) said: “There is no concession allowing anyone to fast on the days of al-Tashreeq except the one who does not have an animal to sacrifice.” 

And Allaah knows best.