To many, this may seem like the best approach ever or the craziest approach ever.
Really, I can see both sides.
The original intent by people like John Holt was meant to change the way information was taught to children. He was famous for writing books like The Way Children Learn, and many others during the 1960s-1980s.
These books championed a way to teach the child as a whole person (similar to Charlotte Mason or Montessori Approaches).
The intention was to get back to how children learned in ages past. Meaning school is more of just life experience and life experience teaches us "school" things along the way.

Now, like so many things that started with correct, or at least good intentions, this particular teaching method has gone a bit coo-coo.
I am not saying that everyone who adheres to the teaching method they label "unschooling" has gone too far. But, the unschooling movement as a whole I believe has definitely done so.
What was once about teaching children in the natural way they learn, has become letting children control how they learn and when. And only learn what interests them at the moment.
Can you see the dangers?
Imagine if you put that ideology to their food diet.

Uhhhhhhh, can you say, Willy Wonka anyone?
Yes! Because they would never choose carrots over chocolate or apples over candy.
Because...they... are... children. They are, by definition, not the ones who are supposed to be in charge. Otherwise we should just call them short adults. Adults who are prone to whining and feet stomping no less.
So, while I believe the movement, often credited to John Holt, absolutely had a valid point, it has moved past its original purpose and into homeschool almost at its worst.

I cover this in another area, but the main crux of the issue is that the unschooled child will not have a broad base of knowledge.
They will have been carried by the wind from assignment to assignment and never established a set of skills and foundational concepts that will prepare them, when they actually become adults, to go on and do whatever it is they want to do.

So, approach with caution, but not necessarily discount this method. Just, do your research ahead of time on the particular curriculum to see if it meets your priorities for your student.
(A quick side note, do not assume that you can pick and choose every concept in a given curriculum because you think some concepts or skills are irrelevant right now, but end up being necessary later on. As much as possible, look ahead to what your child will need for future levels so as to not leave your child up a creek without their multiplication tables. Or, something like that.)

In Summary:

Positives:

  • Breaks the mold of the traditional school setting which absolutely does not teach children in the way they naturally learn.
  • Allows parent and child enormous freedom to customize their learning journey.
  • Fits into a fluid schedule for parents with unusual work schedules or callings, (missionaries, pastors, traveling nurses, etc).

Negatives:

  • Goes from breaking the mold to having no structural integrity at all.
  • Potential for gaps in the child's skills and concepts foundation needed for future tasks or interests.
  • Children are not supposed to be in control...duh. There is certainly a place for them to have a say, or to spend time on topics they dearly love. But, special time should be allotted for that, not all the time given to that.