I think it goes into the sense of honor and code respecting Kryptonian heritage and honoring ones parents that Superman had. He could have refused to obey his father and mother but that's not the character. Perhaps too "boy scout" but that's the character. It's pretty much a well worn theme with all the superheroes (save Spiderman) that they can't maintain a secret identity, be a full time superhero and maintain a marriage. It never works. Such is the price they pay.
You can better understand why he did it in the Donner version where it's Jor-El's image that forbids him from being with Lois without giving up his powers. Jor El has such gravitas that its almost as if Kal El is proving himself and his conviction to his father by willingly entering the red sun chamber. The scene bookends very
nicely with the later scene when a beaten and bruised Kal El goes back to the fortress looking to undo what he's done after being beaten up at the diner. The scene doesn't cut off when Clark finds the green crystal. Clark screams for his father and his body language is that of a shamed and humiliated child even though he's this great big hulk of a guy. Then Jor El actually appears as more than image and.....it's powerful. Donner fought for Brando to stay in the film, but the Salkinds weren't willing to pay. Shame. It was such a wonderfully human father/son moment. Ultimately Clark pays a heavy price for not having listened to Jor El in that scene. It's my favorite scene in the Donner cut.