Well, to explain this I think there needs to be a bit of an understanding behind what a disciple and a personal student are.
Let us first start with the idea of a disciple.
A disciple can be considered a more traditional form of relationship that existed even before the Academy existed. The majority of cultivation techniques, battle techniques, skills, were extraordinarily complicated and potentially dangerous if attempted haphazardly.
This meant that with the exception of a few freaks who managed to forge their own path through blood and tears, the majority of cultivators needed someone to guide them onto the path of cultivation.
Of course, the majority of people weren't so lucky to have someone personally impart a path for them. At best they'd be given a copy of a cultivation manual and a basic demonstration of what to do, after that they were on their own.
The relationship in this instance can be considered that of an outer disciple or with the advent of the Academy, an introductory teacher.
There's no strong relationship in this instance, at most a small debt of karma to the person who introduced you to the path of cultivation.
Next, are people who received personal guidance and tutorship. This could be considered the most traditional master-disciple relationship.
Then there is the personal disciple, or legacy disciple. Typically picked out of the normal disciples, these could be considered the cream of the crop. For these disciples the master would withhold nothing, including their core legacies and resources.
They could be considered the favorite children. This was the type of relationship where the phrase, "A teacher for a day, a father for a lifetime" was most applicable. The relationships between master and disciple were often stronger than the relationships between a child and their parents for people in cultivation sects, as many children with good potentials leave their families at a young age to learn cultivation. By the time they achieve some level of success, forty or fifty years may have passed, and their mortal parents may have already passed away due to one reason or another.
Of course, you can probably see some of the issues with this form of education, the most obvious of which is that a person's time and energy is limited. A master doesn't just exist to teach their disciples, they still have to cultivate, to work on their professions, and to work on sect matters in many cases. Thus, after spending some time on their personal disciples, they don't have that much time for their ordinary disciples, much less the outer disciples.
This lead to situations where a disciple might come upon a bottleneck in their cultivation, something that would be very easily resolved with a bit of guidance, but they have to wait months or in some cases years before getting the advice they need to progress further.
All in all, this was a method that only prioritized the elites and ignored all the rest.
Then came along the Academy's learning structure. Based off of one's talents and interests, students are assigned to different classes in their first few years. The majority of students will be allocated to normal teachers. While they might not be as powerful or capable as some of elders and masters in the sects, at the very least they were readily available and were a stockpile of information that could help avoid any mishaps in the early stages of cultivation.
Later, as the students progress forward and became stronger, they were able to join more advanced classes and electives. If they showed good results they could get spots in the Star Teachers or Grand Teachers classes. Li Chang Hu, for instance who had been a star teacher in the years prior and recently become a Grand Teacher had a significantly better understanding towards cultivation and a few professions of choice than his brother Li Chang Yin. Getting personalized guidance from him could be considered twice the reward with half the effort in the path of cultivation.
The relationship between any teacher and student in their class was just that, they can only be considered normal teachers and students. For instance, even if Fu Hao Xin hated Li Chang Yin, he couldn't shake off the title of being one of his students, as Li Chang Yin had indeed helped impart the path of cultivation on him.
But at the same time as long as he endured for a year or two he'd be allocated to another class and their relationship would end there.
A personal student on the other hand was simply a student that the teacher took a fancy too and gave additional assistance and guidance to in a personal/private manner. This relationship wasn't as close as that of a personal disciple, but could be considered a step above being a simple student.
Fu Hao Xin after splitting up with Di Tou the day before had headed back to class to see that class had been canceled for the week. Due to class being canceled the students were in a rather good mood as Li Chang Yin was a rather strict and boring teacher, and thus he had managed to get away without any additional conflict.
After returning back to his abode, Fu Hao Xin thought about it for a long time and deduced the only reason Li Chang Yin could have canceled class was Senior Mu. Further, thinking about the way that Senior Mu had stood up for him and thrown out a superior grade spirit stone just to help him, he couldn't help but feel a sense of warmth.
So after thinking about it a whole night, he had decided to try to beg Mu Di Bai to take him in as a disciple. After all, he had already seen that Li Chang Yin had no interest in helping him, and he had already somewhat given up on the Academy, so why not hope that Mu Di Bai would help him out a bit?
Having decided this in the heart, he headed out early in the morning to the location Di Tou had told him the day before with a heart full of hope.
After the subsequent events that took place, he couldn't help but put Di Tou on an even higher pedestal, and suddenly felt rather shameless asking for a spot as a disciple, he felt like he couldn't match up to the status he was asking for.
Thus we came upon our current situation.