What they want, what the law forbids, and what non-believers find objectionable is the intentional use of the power of government to give the impression that there is, in fact, a state religion and that everyone needs to conform or risk ostracism or worse. Such "official" prayer sessions are meant to give that impression and also to give the impression that everyone believes and there is no dissent, that dissent is unacceptable and even criminal or insane.
The juxtaposition of the following news items makes this nefarious intent clear:
First, a recent survey of religious websites shows very clearly that prayer itself is not actually that important to the religious either as a ritual or a marketing tool. Even though the religious give the impression that they need to pray the way a chain smoker needs a cigarette whenever the topic of government sponsored organized prayer comes up. One would think that religious people need to pray before almost any activity. In fact, it is the circumstances that cause this sudden alleged need for prayer. Their own publications show that they don't really need to pray before every activity or even that often.
As I pointed out before, the actual impetus behind the sudden need to pray just because the school day is starting is the desire to show unanimity and give the impression that the power of government supports religion. Why is school prayer so important? Because it is an essential part of the brainwashing process. The comments of an Illinois state representative (Ms. Monique Davis) to an atheist witness who appeared before her committee make this clear.
In addition to repeatedly telling him he had no right to be there because he was an atheist and repeatedly ordering him to get out of his seat and leave, she dropped this revelatory little bomb:
"[I]t’s dangerous for our children to even know that your philosophy exists!"
There you have it. An explicit statement of the real reason religious people fight so hard for school prayer: To make sure their kids don't start thinking for themselves, to make sure that they only know of thoughts that support religion, to make sure their brainwashing is uninterrupted, to make sure they don't start asking questions that their parents, teachers, and clergy can't answer.
She is half right. It is dangerous--but not to the children. It's dangerous to the profits of that huge criminal business called religion. If the brainwashing process is interrupted, a huge number of potential tithers will leave the church before they ever start to earn money.
I can speak from personal experience that simply learning that not believing is a possibility can have the effect of causing a child to cease believing. Once you know that it's possible to be a non-believer, you have to ask yourself why you should continue to believe. The honest answer is that there is no good reason. Many children will recognize this because they have received some training in skeptical thinking. When their parents and clergymen explain why other religions are nonsense, they sometimes unwittingly give them tools that can apply with equal validity to all religions.
It is no coincidence that the comments of Ms. Davis precisely echo the rationale given for executing "heretics" back when the religious could get away with it:
"Theodore Beza argued in defense of burning Michael Servetus that when a heretic committed blasphemy and impiety, scorning God’s Word and resisting all attempts at correction, the death penalty was fully justified. Indeed, it was required, so as to stop heresy from 'infecting' other people and destroying the church from within."