Praise be to Allah
Hajj is only obligatory for the one who is can afford it and has the physical strength to do it, because Allah, may He be exalted, says (interpretation of the meaning):
“And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allah, those who can afford the expenses (for one’s conveyance, provision and residence)”
[Aal ‘Imraan 3:97].
For more information please see the answer to question no. 11534.
If the son is able to do Hajj, in the sense that he can afford it and has the physical strength to do it, and he is able to go for Hajj, then he must do that, and if his parents tell him not to or to delay it, he does not have to obey them in that regard, because it is obligatory to do Hajj immediately.
Ibn Qudaamah (may Allah have mercy on him) said:
The father does not have the right to prevent his son from doing the obligatory Hajj, or to make him exit his ihram, and the son should not obey his father by refraining from Hajj, because the Prophet (blessings and peace of Allah be upon him) said: There is no obedience to any created being if it involves disobedience towards Allah, may He be exalted. But the father may prevent him from going out for a voluntary Hajj, because he may prevent him from going out on military campaign, which is a communal obligation, so in the case of a voluntary matter it is more appropriate that he should be able to prevent him from doing it.
End quote from al-Mughni (3/284)
For more information on the obligation to do Hajj immediately, please see the answer to question no. 41702
Becoming financially able to do Hajj is not obligatory, so the individual is not obliged to work or save up money in order to do Hajj, because that without which something does not become obligatory is not itself obligatory.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
That without which something does not become obligatory is not obligatory for a person to do, according to the consensus of the Muslims, whether it is something that he could do or not, such as becoming able to do Hajj, or earning the minimum amount of wealth at which zakaah becomes due (nisaab). If a person is able to do Hajj, then he must do Hajj, and if he owns the minimum amount of wealth at which zakaah becomes due, then he must pay zakaah. It is only obligatory if that condition is met, but he does not have to become able to do Hajj or to acquire the minimum amount of wealth at which zakaah becomes due.
End quote from Dar’ Ta‘aarud al-‘Aql wa’n-Naql (1/212)
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
Is it obligatory to accumulate wealth so that he may pay zakaah, and if one year has passed since his wealth reached the minimum threshold (nisaab), is he obliged to pay zakaah?
Answer: he does not have to accumulate wealth in order to pay zakaah on it, but if one year has passed since he acquired the minimum amount of wealth (nisaab), then he must do what is required to pay zakaah.
The difference between the two is that that which is required in order for something to become obligatory is not obligatory in and of itself, whereas that without which the obligatory act cannot be done is itself obligatory. Acquiring wealth in order to pay zakaah means acquiring that which is required in order for zakaah to become obligatory, and doing that is not obligatory.
A similar case is that of Hajj. Do we say that the individual is obliged to accumulate wealth in order to do Hajj? Or do we say that if he has wealth, then let him do Hajj?
The answer is: If he has wealth, then let him do Hajj; as for the former, that is not obligatory.
End quote from ash-Sharh al-Mumti‘ (6/96).
To sum up the above:
So long as you are not able to do Hajj, and you do not have the necessary funds to do that, then Hajj is not obligatory in your case. It is also not obligatory for you to work and accumulate sufficient funds to spend on Hajj. And it is more appropriate to note that you do not have to give up your studies for the purpose of working and accumulating wealth.
Based on that, you should give precedence to your parents’ wish that you go to university, and delay the idea of Hajj until Allah makes it easy for you to attain the means of being able to do it.
For more information on the guidelines on what is and is not obligatory with regard to obeying parents, please see the answer to question no. 214117
And Allah knows best.