Question

Happy holiday!
I wanted to ask about the authority of someone who is officially my rabbi—whether because I accepted him upon myself, or because for technical reasons I belong to his community.
The words of the Chazon Ish are well known: "It seems that when it is said that in matters of Torah law one follows the stricter opinion, that is only when neither of them is his rabbi. But if one of the sages is his rabbi, he follows him even leniently. And he is considered his rabbi whenever he is close to him and regularly hears his teachings in most commandments.
And in this matter, if there are two sages close to him, he has permission to hold by the rulings of one of them and to regard him as his rabbi. And this is what we say: one who wishes to act in accordance with the words of Beit Shammai may do so—that is, to regard them as his rabbi and to follow them consistently, whether for leniency or stringency.
And this law applies both during the sage's lifetime and after his death, so long as his rulings and laws are known through his students or through his books. Thus, people are permitted to follow their rabbi even leniently in matters of Torah law, even if those who disagree with him are many…"
So what is the logic behind permitting me—or obligating me—to always follow his rulings? Why am I halakhically bound to him, such that if I acted in accordance with him in cases A, B, and C, I am obligated (or permitted) to act in accordance with him in case D as well? I would appreciate it if you could explain it to me or point me to a logical explanation.