1. Honor thy father and thy mother. When your child listens to and follows your instructions, they fulfill the fourth commandment. By respecting your authority as their teacher, the child remains the student which is their calling as a child. If another sibling interjects (especially something contrary to what you've said), the student may falter in their acceptance of your guidance.
2. Being told. Let's face it. Nobody likes being told what to do. It's even worse when you have several people giving you the same instructions. (This is why familial discipline belongs to the parents only. It is not the child's place to discipline their siblings, but that's a topic for another post.) If you are teaching a child (particularly in a subject they dislike), receiving instruction from you is plenty. Having a sibling interrupt with comments on how they would teach it, how the child should learn it, and how it's "so easy" can overwhelm the student to the point of shutting down completely. The learning child will no longer be willing to even try if they believe they cannot succeed. A sibling's peanut gallery comments do not help.
3. Train of thought. It has been my experience that siblings' interjectory comments come at the most inopportune moments, most often right in the middle of your explanation. Being an adult raising children, it can often be difficult to regain your train of thought once it is derailed. This is confusing for the child being taught and frustrating for you. Couple this with your already short temper (unless you happen to be an angelic mother who doesn't have frayed nerves), and you have a recipe for disaster. I know you cannot avoid all interruptions (especially with numerous children), but the fewer you have, the easier school will go.
All in all, keeping the instructions solely within your realm of authority is a good idea. I do not, however, object to useful comments from siblings. While these comments should not arise in the midst of instruction, oftentimes a sibling's observations can lend a new light to your potential difficulties in teaching. Please ask your children for suggestions regarding new ways to make learning more interesting. I have often given my two cents worth regarding various school subjects (most especially Latin), and I like to think that my personal experience with home schooling through high school lends a bit of authority to my musings. I can only relate what I have learned or observed for myself (which I know cannot apply to every person), but I hope that some principles remain the same throughout all learning children. If you have taken up the wonderful cross of home schooling, don't be afraid to ask for advice, even from your children. Just make sure that while the teaching is actually happening, your children remain simply students. Let them enjoy being a child without having to teach their siblings. If they won't fight for their right to learn and not instruct, then you must.