Many of the speech proponents emphasized that the speech was non-political and only contained a positive message that all students could benefit from - but they are missing the point. The point is whether or not the President should have an audience with children at any time during school without their parents' involvement.
Children attend school for the sole reason of obtaining their education. They are not there to be at the beck and call of the President. Children are not allowed to vote because they don't have an understanding of the world or the bigger issues. They need to learn them before making an informed choice about what the president is saying. Adults can listen and process a Presidential speech, but children cannot. And kids in a classroom have no choice but to watch, and watch without their parents' input. In this way, the President has circumvented the parents.
When Obama wants to speak to children without the parents' involvement, it looks like he's trying to gain some influence over them in some way. Kids tend to indulge in "hero worship" more than adults and seeing the President speak directly to them, without parents, creates a special sort of relationship that the child has with someone without the parent being involved - it could be their first experience with politics and based on that speech they could be swayed to his side of the issues. It also sends a message to the parents. "You might be the parents, but when your child is at school he belongs to the state. We will teach him without your influence." Parents aren't allowed to watch the speech with their kids and provide their comments or opinions.
It also sets the precedent that the President has some sort of control or authority over children. He can speak to them whenever he wants and they have to drop what they're doing and listen. They stop their day to listen to the President - why? They aren't military personnel; they aren't government employees; they aren't even taxpayers - they are students. So why do they have to drop everything and listen? Adults don't have to stop what they're doing to listen to the President but these kids do, and it sets the precedent that they will again when they grow into adults.
It totally sends the wrong message to kids. Citizens elect the President. The President works for us. He has to listen to what we have to say. His job is to ensure Americans' best interests are represented in the world. So to force kids to drop what they're doing and watch his televised speech sends the message that he's like a King and we're his subjects. When the horns announce his presence we all must bow and listen. I'm exaggerating this to make a point - people in a free society do not have to drop what they're doing to listen to a Presidential speech and that includes children.
I personally think Obama wanted to give this speech to test the waters. He wants to push to see how far he can reach without receiving a backlash, which isn't the first time he's done so. He asked Georgetown University to cover the name of Jesus Christ while he spoke there. It was also requested that the Naval Academy grads not wear their ceremonial swords while Obama spoke there. Both of those examples are of him asking someone/something to do something that is inherently against their philosophies/traditions. Obama knew asking to nationally televise a speech to school children would make people slightly uncomfortable, but not enough to not let it happen. Then, if the speech went over well enough he could make it the "norm" to speak to children whenever he wanted to. Maybe even create a monthly or weekly address.
So the content of today's speech wasn't a big deal at all. It was never about today's content. It was about the fact that the President could speak to your children at will, and set a dangerous precedent that it's okay to drop what you're doing, listen and obey.