Graduation ceremonies are full of all sorts of traditions, including moments of silence and reflection, and sometimes student prayers. Prayer or moments of reflection are a traditional part of MANY solemn occasions and rites of passage. I know this may sound bizarre to some people, but a huge chunk of the population feels that these traditions are important - and a moment of silence is a huge compromise to them.
The rigidity of not even being open to a moment of silence to REPLACE a tradition that is very important to some people is extremely counter productive and creates a situation where people will dig their heels in harder.
In other words, the lack of a willingness to compromise seems unnecessarily inflammatory, when emotions on both sides of the issue run high.
Patience, tolerance, mutual respect, kindness, generosity. A big dose of each would be very beneficial in such situations.
I don't necessarily disagree with you, but many of those traditions you're referring to were born in a time when being openly atheistic, secular, of a different religion, or even just the wrong brand of Christianity, was taboo and in some societies might even get you killed. Obviously I'm speaking in a context of North America and Europe.
There are many societies like that today still. If I went to Somalia or Saudi Arabia and said openly I didn't believe in God, I'm sure I would have a few AK-47s up my rear before I could say "Hosannah". The biggest progress of our society was when we started to have greater embraces of secularism. Nobody is oppressed. Religions/religious people don't need to be excluded. No minority in the country is forced to be subjected to the rituals and customs of a different group if they don't want to be.
Naturally, some Christians are against it because they feel since they are (for now, at least) in the majority, their religion and customs should be thrusted upon everyone else, whether or not other people want to be subjected to it. The beauty of secularism is that nobody needs to be forced onto anything.
Indeed, in the context Canadian society, I was forced by my parents to attend Catholic schools and take part in Catholic ceremonies and masses. I was a Catholic growing up because they told me I was Catholic and that's all I was taught, but when I was finally given an opportunity to think for myself, I found it very difficult to openly express my atheism because everyone around me was Catholic and regularly expressed disapproval and even hatred towards atheists. If I questioned Catholicism too much, I would face consequences. I don't want my children to grow up in a society like that.
Another side of the coin, is that speaking from American and Canadian societies, how many ceremonies and events open up with a Muslim, Jewish, or Hindu prayer? They are almost always Christian prayers. That's a result of demographics, but also culture and history. But why continue culture and historical practices when it excludes others? I'm not offended by anyone else praying to whomever they wish, I just don't think anyone else should be subjected to it. You don't need to pray at a ceremony that has a purpose of honouring graduates.
I'm open to a moment of silence - I think it's an excellent first-step. I just don't see why prayer needs to be a group effort and that everything has to stop to accomodate it. I don't understand why if you're a Christian or whatever religion you wish, you simply can't just fold your hands, bow your head, and mutter your prayers to God to yourself. I still view it as totally unnecessary.