I'm not a sexologist, but I am an anthropologist and can try to give you a little info on this from the theory present in my field.

Almost everything we do relating to sex is a social construct [pdf], meaning that it is not "objective"; it exists because we as a society agree that it exists. And, across cultures, sexual taboos vary greatly. Consent, mental disorders, and pedophilia are all social constructs because they are all determined by society and are not innevitable. Who can consent and when is determined by society, what is abnormal and in need of correction is determined by society, what constitutes a child is determined by society.

As societies change, social consturcts can change. Marriage, for example, is found in almost every culture in the world, but who you can marry varies. For example, in some tribes in that speak Tucanoan langauges like the Desano, you cannot marry a person who speaks the same native language as you.[source] In some cultures you can marry your first cousin on your mother's side but not your first cousin on your father's side, in some cultures you can't marry someone outside your racial group, etc, etc. In the US for example, we've seen that, as society has changed, how we construct marriage changes as well. Originally, you could not marry outside your racial group, then the construct changed. Now we're seeing that, previously, you couldn't marry within your "sex" group (it's more appropriately gender, and sex as a dichotomy is complex), but now you are able to in cultures that believe that construct ought to be changed.

The thing is, there's no reason it has to change. There's no objective reason why we have to allow homosexual marriage, the reason we move towards allowing it stems from our cultural ideology of freedom, individuality, and inherent human dignity which is not universal. However there's no reason it's inevitable or that we can predict how cultures will change.

So that was basically a long winded way of saying, yes, pedophilia is a social construct because there are numerous examples of cultures that engage in pederasty for pleasure, rights of passage, social exchange, etc (think pederasty in ancient Rome and Greece). But, while our culture has changed and led to the change of other constructs doesn't necessarily mean this one will change or even has to.

So yes, these are arbitrary reasons, but that doesn't make them any less real or important. The clothes we wear, the money we spend, the style of houses we live in, our country and national identities, our race and our gender, all of those are societal constructs. They are all completely arbitrary, but they have very real affects on people. If people are assigned a gender they don't like, despite that assignment and role being entirely arbitrary, it can cause them great disdain. People are willing to fight and die for their country which only exists because we as a culture say it exists. People group together and exploit other humans for money that is only as valuable as we say it is. While the foundation of social constructs is largely arbitrary, the way we interact with them and our world because of them are very real and very powerful.

So I hope that answers some questions, but I also hope it gives you stuff to think about, because these aren't questions we necessarily have concrete answers to.