Many of the biggest proponents of critical thinking are themselves converts from authoritarianism. Raised in families in which authority was simply asserted, they went off to school where they were taught to think critically about all authorities, whether texts or people. Thereafter they regarded themselves as liberated from authoritarianism.
And then they had children. They were put into the position of authority. What to do? Many first-generation critical thinkers went overboard the other way. On principle, they never told their children what to do, never said no. They didn't teach their children any religious faith, in hopes that the kids would make up their own minds. They didn't make their kids read any good books, for fear of imposing a standard of goodness by authority. Likewise, they didn't forbid their children any books, movies, games, etc., for fear of stifling their creativity.
But the basic fact is that children need authority. They need limits, crave structure, beg for authoritative teaching. You can't raise kids to be critical thinkers permissively.
How do you raise critical thinkers? Use your parental authority to teach your children to question authority.
I use the simple expedient of telling my children outrageous falsehoods every day. From "good morning, chicken head, what lovely feathers you have today," to "lights outs, beloved; research has shown that sleep-deprived children develop tails," my kids are subject to a constant stream of, shall we say, critical thinking opportunities. They usually respond with reasoned arguments demonstrating that dad is obviously mistaken, again. Gradually, they are also developing wittier parries to these paternal fibs. This makes for a happy home, though it is sometimes disconcerting to visitors.
So, if you love you kids, lie to them. They will think you for it later.