Why there? What does כיבוד אב ואם have to do with Beis Din?
בשעה שאמר הקב"ה אנכי ולא יהיה לך אמרו אומות העולם לכבוד עצמו הוא דורש כיון שאמר כבד את אביך ואת אמך חזרו והודו למאמרות הראשונות
When G-d said "I am" and "You shall not have" the nations of the world said - he is demanding his own honor. Since He said "honor your father and your mother" they relented and agreed to the first sayings.
He suggest the connection is about honoring G-d and the importance of the mesorah. But perhaps another way of looking at it is that during Hilchos Mamrim, you could read it as Beis Din and Rabbonim demanding their own honor, so the Rambam includes it here to show that Halacha demands the honor of others (e.g. your parents) as well.
If you want a minimalist answer, the fourteenth section of Mishneh Torah (as stated in the introduction) is about things given over to the Sanhedrin. One Halacha in Kibbud Av V'Em are about limitation on a person when dealing with their parents as emissaries of Beis Din (5:13) and a בן סורר ומורה has to be brought to beis din by his parents (unlike anything else where the witnesses go themselves), so both those matters in the general idea of Kibbud Av V'Em are related to matters of Beis Din, so the Rambam includes all of it here.
It's about respecting authority. First the authority of our legal system, then the authority of parents.