Is it the question as stated, or the problem that's obvious?
Personally, and as a moderator, I think the important part of a question is the question the OP asked, because what is an obvious problem to you may not be a problem to the OP.
A good example of this is "crying it out". Parents have different beliefs about allowing a baby to cry it out (cry themselves to sleep.) I don't advocate the practice. However, it's been taught for generations and is still a big part of parenting cultures around the world, and this is a global community. If a parent asks a sincere question about CIO, I believe the respectful thing is to not answer if some helpful advice can't be given.
"You're a barbarian if you let your baby cry it out!" is an example of an unhelpful answer, and unfortunately it's not an unusual response to such a question. It assumes the culture one identifies with is the only correct one. Often it's more kindly put, but still involves negative judgement not only of the practice but of the OP as well.
Because this is a recurring issue, we've had numerous meta questions discussing answers such that disagree with the premise:
What should moderators do with answers that disagree with the premise of the question?
What is the ideal response to a question based on a premise one does not accept?
How to respond when a parent is asking about something that is abuse?
When is an answer not an answer?
What is the policy/rules on answers that are rooted in negative sides of single parenthood?
The answer has been, if you can't agree with the premise of the question, skip the question.
Some people are unable to do this, and feel it is their duty only to educate the OP about their error. A recent example was about spanking. I thought it was interesting and worthy of discussion. When is spanking effective, and if it's OK to use corporal punishment at 5, why is it not at ten? I think there is a respectful way to answer the question which incorporates both views. However, most of the answers were not respectful.
A recent example of when an answer doesn't address the question was this post by an unmarried but culturally religious woman anticipating problems raising her children with her atheistic partner to whom she was not yet married. I don't think the OP was asking if she ought not marry her significant other, yet some of the answers did suggest that, and most were answers along the premarital counseling route. But not one answer concentrated on her question.
I assume the above is an example of what you are referring to when you mention "the problem that's obvious". (Please correct me if I'm wrong.)
I don't want this to be a site that shows disrespect for OPs who ask sincere questions on a topic with which we happen to disagree. Luckily, this is the current opinion of the moderators, as well as the advice most often given by the Community Managers.
It would follow then that the most important part of an answer is the part that deals with the question asked.
However, having said all this, one can answer a question the premise of which one disagrees, and put in a respectful alternative as an aside. If the aside is the entire answer, it's not really an answer to the question.
I think the time may have arrived to revisit this question as a community, as there have been several questions in quick succession that invited many answers disagreeing with the premise. Either people don't agree with the guidelines or choose to disregard them. When it happens too often, it puts the moderators in an awkward position.
If you asked a sincere question about for tactics to raise a child in your religion when the world around them seems to favor atheism, I don't think you would welcome being told you were an idiot to believe in an invisible, unkind and unloving higher power akin to the flying spaghetti monster. Yet it's been done. If you were trying to deal with how to motivate a child who struggles with schoolwork, you probably don't want someone to tell you schoolwork is stupid, and useless in the real world, yet it's been done. Many such answers have been given because people have different belief systems which they believe are the only correct one.