Seung Yoo returned to Asung High in Melancholia for the same reason that Yoon Su did. She had left Asung High to teach students in villages and towns far away from Seoul. She returned as a coordinator -- a person who helped students with influence and money get admissions to ivy league colleges in and outside South Korea, to ensure that Noh Jung Ah's truth was revealed in Melancholia.
Caution: This article contains spoilers!
Both Seung Yoo and Yoon Su were aware of the fact that Noh Jung Ah had used Ye Rin in the past in Melancholia. They were also certain that she was not someone to be taken lightly. Her influence ran deep in Melancholia and to bring her down from the respected position of the principal of Asung High, was not going to be easy.
Seung Yoo wants to work with Yoon, but she refuses in 'Melancholia' episode 9
Seung Yoo returned as a teacher in Asung where he met Yoon Su's student Si An. The girl reminded audiences of Seung Yoo when he was young and Seung Yoo is in the same position that Yoon Su was in, years ago. Si An respected Seung Yoo the most and liked him as a talented mathematician.
There is no romance involved in Si An's feelings for Seung Yoo in Melancholia. She trusts him as her teacher, just as she trusted Yoon Su. So the audience may think that the same complications would not arise as they did in the past. However, the other students wonder why Seung Yoo treats Si An differently.
They also came across a selfie that Si Ah had posted of herself with Seung Yoo after his conference. So her classmates pestered her, asking her if she liked Seung Yoo. She replied that she did, and shocked everyone. Instead, she also stressed that he was the teacher that she respected most.
Will history repeat in Melancholia or can Yoon Su and Seung Yoo stop Noh Jung Ah before she does further damage? The question arose the moment Yoon Su refused to collaborate with Seung Yoo. He had requested that she reveal her plans to him. She, however, claimed that there was no reason for her to trust him and hence she left him with no answer. However, she soon learned that Seung Yoo had a plan of his own.
He planned on using the same reporter who had outed Asung High's corruption in the past in Melancholia. Of course, in the past she was used by Noh Jung Ah's sister, who was fighting her for control of their father's wealth and company. Now, the same reporter was Seung Yoo's contact, and he indicated that he would change into a whistleblower if it meant he could drag Noh Jung Ah from her well-protected throne.
He also had Ye Rin's father on his hit list, and was ready to do everything necessary to keep his promise to Yoon Su all those years ago, He had promised her that he would prove her innocence and that is exactly what he is set to do.