(Note: rough draft state.)
In the 1960's or 1970's a saying became popular, "Question Authority!" A little research on the Internet reveals it may be something from Socrates' teaching. But my opinion and explanation will still remain the same whether Socrates, Timothy Leary, Confucius, or Buddha first said it. (All of those folks, I read, are said to have used the saying or one similar to it.)
Asking questions can be done skillfully. Asking questions is both an art and a science. Lots of people say things they don't mean; that includes statements as well as questions.
Not only is it important to choose the words that clearly convey what you mean, but knowing how to ask your question is often important. Tactfulness is often appreciated.
Some people have a very large opinion of themselves, those folks tend to be the people who can't handle being asked a question in a manner they think is disrespectful. How will you know? They will blow up, emotionally, in your face; they will demean you, and probably not answer the question.
Other reasons folks may avoid answering questions include: questions they think are unfair, a misleading question meant to entrap them, or perhaps they just recognize the question as Un-Constitutional. Implying that if they answer the question they will incriminate themselves, and if they don't answer the question, they incriminate themselves as though they are trying to hide information.
So the "moral of the story" of the above is that even though you ask, you may not immediately receive.
Some people may try to get you to believe you should just accept everything handed to you. Many of those people are the ones with a too high opinion of themselves and blow up when you question them.
Some people think God must have the biggest ego of all, since he is God, The Creator. This isn't the case. God welcomes your questions, ALL of your questions.
This may seem too much for some folks. Folks may claim that, "God is so ______ that God would never stand to be insulted to God's face." But I say that as long as they face God and go towards God, they will be healed; as they get closer to God, they will change, and will stop asking insulting and/or mean questions.
God does not get mad when people who don't believe in God question God. God told Yeshua/Jesus to proclaim "ask and receive". If you ask, you will receive; even if you are not a believer in God.
See note 1.
It is not subversive to question authority, it merely shows that you do not understand something, or would like to know more about it. Or maybe the "authority" in question is trying to hide something, and has contradictory explanations of what it's doing. In any case it's still a good idea to question authority.
In general, I advocate thinking about your questions beforehand. Consider it a rough draft to do so. Some questions might be better if worded differently, or it might be better to break a question down in to a few questions, and ask them one at a time.
As you formulate your questions, notice any assumptions you could be making. I feel certain folks have asked you questions in the past you thought unfair, because their question supposed something that wasn't true. (For example, your mom walks in the room and says, "When did you break the cookie jar?" But it was your sister who broke the cookie jar, so you see, her question assumed, incorrectly, you broke the cookie jar.)
Some times are better than others to question authority; I highly recommend not being antagonistic towards the folks you ask questions of, show them the same kind of respect that you would like to be shown.
In conclusion, I highly recommend questioning authority. That doesn't necessarily mean you question why they are in authority, of if they have authority, but that you ask them questions.
It is not disrespectful to ask questions about God, or to God. Jesus recommends it. It may not seem that way, but God does not harbor any contradictions, his character is totally true and honest. (See my writing on Some Simple Beliefs About God.) Need another example? Jesus said the kingdom of heaven belongs to ones like little children [Luke 18:16]. What are little children famous for? Among other things, asking LOTS of questions.
Note 1 (Brief qualification...even believers do not get instant answers to their questions, sometimes it takes a while for the answers to be discovered. Sometimes it takes a long time to figure out how to ask the question better, or recompose the original question as a series of related questions. It is also important to not test God, or ask him for signs. This is even considered rude by humans. What do I mean by testing or asking for signs?
Simple, do not put God to the test, do not say things like, "God, if you exist, then save me from death as I test your existence by jumping off this cliff." Why? Because frankly, you should have more sense than to jump off a cliff to test if there is a God or not. Also, do not say things like, "I'm not sure who to vote for. Give me a sign if I should vote for X or Y." We all have to make decisions we're not entirely sure about, don't ask for signs from God.) [Mark 13:22, Matthew 16:1-4 ]Unrelated extra... One of the saddest lines in the NT Gospels, to me, is where it says, "And no one dared ask him any more questions." [Matthew 22:46, Mark 12:34, Luke 20:40].