He gets angry and does not speak to his parents and does not make up with them

Firstly: 

The rights of parents are great indeed.
Allaah mentions parents’ rights in conjunction with His own rights in many verses, for example, when He says (interpretation of the meaning): 

“Worship Allaah and join none with Him (in
worship); and do good to parents”
[al-Nisa’ 4:36] 

“And your Lord has decreed that you
worship none but Him. And that you be dutiful to your parents”

[al-Isra’ 17:23] 

“And We have enjoined on man (to be
dutiful and good) to his parents. His mother bore him in weakness and hardship upon weakness and hardship, and his weaning is in two years

give thanks to Me and to your parents. Unto Me is the final destination”

[Luqmaan 31:14] 

And there are many similar verses. These
verses indicate that it is obligatory to honour our parents, treat them kindly and thank them for their kindness to the child when he was in his
mother’s womb and until he became independent and could take care of his own interests. Honouring them includes spending on them when they are in
need, hearing and obeying them with regard to things that are good and proper, lowering the wing of humility to them, not raising one’s voice to
them, and addressing them with good words and politeness, as Allaah says in Soorat Bani Israa’eel: 

“And your Lord has decreed that you worship
none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of
disrespect, nor shout at them but address them in terms of honour.

And lower unto them the wing of submission
and humility through mercy, and say: ‘My Lord! Bestow on them Your Mercy as they did bring me up when I was young.’”

[al-Isra’ 17:23-24] 

 In al-Saheehayn it is narrated that
the Prophet (peace and blessings of Allaah be upon him) was asked which deed is best. He said, “Prayer performed on time.” He was asked, then
what? He said, “Honouring one’s parents.” He was asked, then what? He said, “Jihad for the sake of Allaah.” 

And he (peace and blessings of Allaah be
upon him) said: “The pleasure of Allaah is in pleasing one’s father and the anger of Allaah is in angering one’s father.” Narrated by al-Tirmidhi,
1821; classed as saheeh by Ibn Hibaan and al-Haakim, from the hadeeth of ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas (may Allaah be pleased with him). The
version narrated by al-Tabaraani refers to “parents” (instead of “father”). And there are very many ahaadeeth which state that it is obligatory to
honour one’s parents and treat them kindly. 

The opposite of honouring them is disobeying
them, which is one of the major sins, because it is proven in al-Saheehayn that the Prophet (peace and blessings of Allaah be upon
him) said: “Shall I not tell you of the greatest of major sins?” – three times – and we said, “Yes, O Messenger of Allaah.” He said: “Associating
others in worship with Allaah, and disobeying one’s parents,” – and he was reclining, but he sat up and said, “And false speech and false
witness.” Narrated by al-Bukhaari, 2654; Muslim, 126.  

In al-Saheehayn it is also 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:
“One of the major sins is a man insulting his parents.” It was said, “O Messenger of Allaah, do people really insult their parents?” He said,
“Yes, a man insults another man’s father so he insults his father, or he insults another man’s mother so he insults his mother.” Narrated by
al-Bukhaari, 5973; Muslim, 130. So the Prophet (peace and blessings of Allaah be upon him) regarded causing one’s parents to be insulted as
insulting them. So every Muslim man and woman must pay attention to honouring his or her parents and treating them kindly, especially when they
grow old or are in need of kindness, honour and service; and they should beware of disobeying them or treating them badly in word or deed. 

From the words of Shaykh ‘Abd al-‘Azeez ibn
Baaz (may Allaah have mercy on him), 8/306, 307. 

Secondly: 

Remind your brother of Allaah and tell him to
fear His punishment; show him the texts that warn against disobeying parents and explain to him the status of honouring parents in Islam, so that
proof will be established against him and you will have discharged your duty before Allaah. He should realize that he is sinning because of his
abhorrent treatment of his parents and he is doing something that Allaah has forbidden. But despite that do not despair of his being guided, and
do not give up on trying to reconcile between your brother and his parents. But if you are unable to do that, then Allaah does not burden any soul
beyond its scope. 

Strive to find different ways of offering
advice to your brother, sometimes by letting him hear a moving tape, sometimes by giving him a useful book on this topic. And you have to remind
him that Allaah may punish him through his children, because they may do the same to him as he is doing to his parents now, and so on… 

Another way of dealing with this is to look
for the causes that are making him behave like this, then try to resolve them. It is clear that there are some psychological problems affecting
many of those who disobey their parents, such as delaying marriage, or the presence of some evils in their homes that cause them to be disobedient, and so on. 

And Allaah knows best.