The way I read it, it's not about asking permission, per se, it's about setting expectations. "Head's up, I'm about to disagree with you." Also by giving them this ability to "opt in" to the disagreement, you're creating a relationship based on trust. In other words, they're hearing you respectfully express your thoughts and feelings, and that makes them _more_ likely to listen to you in the future, versus just barging in with your thoughts unannounced. (Contrariwise, if they say "no" too many times, then they don't trust you or your opinions -- and that's information for you to do what you wish!)
And sometimes? Your boss doesn't want you to disagree, they just want you to execute, saving both of you the time and energy of arguing.
You may still disagree, and you may not like their decision to just execute, but at the end of the day, they're the boss and you aren't. You're free to get another job!
As a leader in my company, I welcome disagreement early on. But at some point, we have to execute and we can't get stuck in a stalemate because I want A and you want B. Someone has to make a decision, and as the superior, that responsibility lies with me (or in some contexts, it lies with my superior, even if I disagree!).
(P.S. You are allowed to disagree with your parents, too!)