Edit: I want to add a detail to further clarify this point. In the famous story brought in sefer Shmuel I chapt. 18, it describes Yonason sitting at a seudah with his father Shaul Hamelech but with Dovid missing. (This is the haftarah of "machar chodesh.")
In verse 25 it says that Yonason sat Avner in place of Dovid, in between himself and his father.
Rashi and the Metzudos bring there that it's not the derech for children to lean next to their father; thus Yonason wanted to have someone in between.
From here the poskim discuss having a child sit next to one's parent. (The Mishna berurah siman 90 brings the chayei adam that child should not sit next to one's parent, the same way a talmid should not sit next to a rebbe muvhak. The minhag is not like this, but rather like the Aruch Hashulchan that I'll bring in a moment.)
The ben ish chai (in his hilchos kivud av v'em, I believe parshas mishpatim shana shniya) discusses this issue. He concludes that it's only a problem of leaning, which is more relaxed. But just sitting next to one's parents is not a problem. (He himself points out that for Pesach when we do lean, it would be a problem to do so next to one's parents.)
The Aruch Hashulchan, in Y.D 240, says that it's only a problem for bnei melachim to be next to their parents. for non-royalty it's not a problem. I saw discussion years back that this could still be a problem for leil Haseder, since on Pesach night we do act as royalty in certain ways.
based on this idea, we can explain why we wouldn't recline next to our rebbeim or our parents at the seder. We recline to show our freedom and cherus. But it's not derech cherus to recline when it would be disrespectful.
Thus when we have a mitzvah to recline leil haseder, but we also have a mitzvah of reverence for our parents and rebbeim, the reverence will win out. It wins out since as long as there is a mitzvah of reverence, there is no custom of leaning and thus no mitzvah to do so.
And of course, once the parents and rebbeim give permission, it goes back to being derech cherus and one must now lean. (Melachim cannot be mochel on their kavod, but parents and rebbeim can as is clear from Y.D. 240, 242, 244 based on the gemara kidushin 32b).