He wants to get married but his mother is objecting to that because he is young

Firstly: 

It is permissible for a man to get married without his parents’ agreement, unlike a woman, for whose marriage to be valid it is essential that her wali (guardian) agrees. But it is part of honouring one’s parents and treating them kindly to ask for their permission and seek their approval, because that is more likely to keep relationships with them harmonious. 

Secondly: 

You should explain to your mother how great your need for marriage is, and try to convince her and earn her approval. If she responds, then praise be to Allaah, but if she persists in her attitude, then there is no sin on you if you get married to the girl you want, if she is righteous and religiously-committed.  

It is a common mistake for parents to refuse to let their children get married on the basis of studies or their being too young; they do not understand the problems suffered by young men at a time when temptation is widespread. Their refusal may lead to their children going astray and following a path of evil. Hence we advise fathers and mothers to help their sons and daughters to get married, and to make it easy and encourage them to do that, in obedience to the words of the Prophet (peace and blessings of Allaah be upon him): “O young men, whoever among you can afford to get married, let him do so, and whoever cannot afford it, let him fast, for that will reduce his sexual energy.” Narrated by al-Bukhaari (5065) and Muslim (1400). 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about someone who wanted to get married but his parents refused. He replied: 

With regard to this issue, we must offer two pieces of advice. Firstly, we advise your father who insisted on not allowing you to marry this woman whom you describe as being of good character and religiously committed. What he must do is allow you to marry her, unless he has a legitimate shar’i reason which he knows and can explain to you so as to put your mind at rest. He should weigh up this matter himself and imagine if his father had prevented him from marrying a woman whose religious commitment and character he liked, would he not regard that as a disgrace and restriction of his freedom? If he would not like his father to do that to him, then how can he agree to do that to his son? The Prophet (peace and blessings of Allaah be upon him) said: “No one of you truly believes until he likes for his brother what he likes for himself.” 

It is not permissible for your father to prevent you from getting married to this woman with no legitimate shar’i reason. If there is a legitimate shar’i reason, then let him explain it to you so that you will understand. 

And our advice to you is: if you can find another woman instead of this woman, and please your father and maintain a harmonious relationship with the family, then do so. 

But if you cannot do that because your heart is attached to her, and you are afraid that if you propose to another woman that your father will prevent you from marrying her too – because some people may feel jealous even towards their children and prevent them from doing what they want – then I say: if you are afraid of that and you cannot do without this woman to whom your heart is attached, then there is no sin on you if you marry her, even if your parents object. Perhaps after you get married he will accept what has happened and what is in his heart will go away. We ask Allaah to decree for you that which is best for you. 

End quote from Fataawa Islamiyyah (4/193) 

And Allaah knows best.