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.