Before I answer, let me make two points. First, I assume that you are asking about banning the teaching of religion in public schools, not about banning all religion. Second, I have no way of knowing which “key reasons” you are aware of or what “higher level examples and viewpoints” would be in your opinion. Therefore, I can only present that I am aware of and let you decide which are “higher level.”
As I see it, there are two main reasons why it would (arguably) be good to teach religion in public schools. First, teaching religion could improve the morals of the students. School is not solely about learning academic content. Instead, schools are supposed to impart “life lessons” to students. By teaching them religion, we could teach them to have good values. This might reduce the incidence of such negative things as drug use and teen pregnancy. By teaching religion in our schools we would (this argument holds) improve our society. Second, teaching religion could improve the level of cohesiveness in our society. When everyone in a society is part of the same religion, society holds together better. People have more reasons to feel connected to one another and to care about one another. Therefore, we could create a more connected and cohesive society if we were to teach one particular religion in our schools.
However, these possible good things come with a major drawback. By teaching religion in public schools, we would be imposing one version of religion on everyone. This would be a major problem in a country that has religious diversity. There are many different Christian sects with different beliefs and each of those sects would probably object to having their children be taught the doctrines of other sects. A Mormon, for example, would not want their kids to be taught Catholic doctrine. Families that are not Christian at all (Muslims, Hindus, Jews, etc.) would be even less happy because more of their doctrines would be different from those taught in school. Children who had different beliefs than those the teacher was espousing might feel very uncomfortable being forced to join in prayers being led by the teacher.
In short, while teaching religion in school might improve morals and social cohesion, it would be very painful for many of the students and parents in a religiously diverse society.