Seeking knowledge, if this knowledge is something obligatory, is not dependent on having parents’ permission, but if it is supererogatory knowledge then it is essential to have their permission. 

Muslim (2549) narrated that ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas said: A man came to the Prophet of Allaah (peace and blessings of Allaah be upon him) and said: “I give you my oath of allegiance, promising to migrate and fight in jihad, seeking the reward of Allaah.” He said, “Are either of your parents alive?” He said, “Yes, both of them.” He said, “And do you want to seek the reward of Allaah?” He said, “Yes.” He said, “Then go back to your parents, and keep good company with them.” 

Seeking knowledge is one of the kinds of jihad. It is not permissible to pursue supererogatory kinds of knowledge which dictates travelling and leaving them, without their permission. 

Ibn Muflih said in al-Adaab al-Shar’iyyah (2/35-36): 

With regard to the one who goes out seeking knowledge, he must go out with the permission of his parents, because the virtue of supererogatory actions cannot be sought without the permission of one's parents.  

Al-Marwadhi said to Abu ‘Abd-Allaah (i.e., Imam Ahmad): What do you think of a man who is seeking knowledge and he asks his mother for permission, and she gives him permission, even though he knows that she would prefer him to stay? He said, If he is ignorant and does not know ho to issue a shar’i divorce or how to pray, then I prefer him to seek knowledge, but if he knows that then I prefer him to stay with her. 

Al-Khallaal narrated that a man asked him: I am seeking knowledge, but my mother does not want me to do that; she wants me to engage in business. He said to me, Do your best to please her, but do not stop seeking knowledge.  

He said to him: I am a stranger in the land seeking knowledge. Is that better or should I go back to my mother? He said, If you are seeking knowledge that is essential then there is nothing wrong with that. 

A man asked him: I have just arrived and I do not know anything, what do you command me to do? Abu ‘Abd-Allaah said to him: You have to seek knowledge. 

Ishaaq ibn Ibraaheem said: I asked Abu ‘Abd-Allaah about a man who has two well off parents and wants to seek knowledge of hadeeth, and they do not give him permission. He said, He should seek as much knowledge as will benefit him, and there is nothing as good as knowledge. 

It is clear from the above that what is meant by the words of Imam Ahmad is: If the knowledge is obligatory then parents’ permission is not essential, and if it is supererogatory then it is essential to have their permission. 

And Allaah knows best.