The definition of pedophilia is somewhat arbitrary, as evidenced by its variation across the several States (using age of consent as an indicator).
In WV the age of consent used to be 12 (maybe still is, dunno). In MA it is one age and in NH it is another. And it isn't necessarily an absolute age, sometimes it is relative age that makes it a crime (two 13 year old kids can have sex with (legal) impunity, but for a 17 year old and a 14 year old is a crime, and the 17 year old can't even neck with an 18 year old).
Who is to say when someone is old enough? So we must have some arbitrary standards, the same way we have arbitrary standards for blood alcohol and safe speed limits.
I disagree with your so-called 'moral argument.' The vast majority of people are revolted by the idea of true pedophilia (as opposed to relationships crossing arbitrary age boundaries where the age differential is not unusual) and view pedophiles as 'sick' while the same is not true of someone dating multiple members of the opposite sex (playing the field, sowing wild oats, not 'going steady') however intimate and durable their relationships.
When I was 16 I was propositioned by a 12 year old and I politely refused. It was not a crime in the country we were in, but outside my personal morality for multiple reasons including her absolute age and physical maturity and also our social relationship. I think she was curious and didn't really understand what she was offering (although the offer was clear). But I viewed it as wrong then and still do. When I was 25 I was dating a 19 year old. A larger age difference, yet a perfectly acceptable relationship. Suppose I had met the same woman 5 years earlier. Would a relationship have been wrong? It surely would have been illegal. And in between 16 and 25 I dated some number of women, with varying degrees of exclusivity, sometimes several concurrently or sometimes only one and never sought to hide the fact from anyone.
So, we have arbitrary definitions for the age of consent but there is an almost universal acknowledgment that there should be rules to determine when a person is adult enough to decide for them self, but no such acknowledgment of rules regarding how many concurrent relationships one may have.
So we must have some arbitrary standards, the same way we have arbitrary standards for blood alcohol and safe speed limits. I disagree with your so-called 'moral argument.' The vast majority of people are revolted by the idea of true pedophilia I certainly agree about standards. But I wouldn't call standards like blood alcohol or consent arbitrary; they are the result of accumulated experience (history) as well as scientific study.
We have systematically studied and quantified the effect blood alcohol level has on reflexes. That's easy to do. Then correlate the data with probability of past mayhem where the driver had drunk, and after allowances for socially responsible drinkers (there may actually be a human gene for wanting a buzz) you can set a workable boundary.
It's harder to do this for cultural mores and proscriptions. We say the child abuse is universally despised.But we've never really studied the issue in any laboratory, remote from cultural influences to verify the claim. We'd probably need a distant planet to colonize for that purpose.
There may be a universal innate reaction we call guilt. But to assume that this guilt is sufficient to control behaviors we now disapprove of now, is wrong. The cannibal who refuses to eat the missionary probably feels guilt.
So, in this realm we only have the wisdom of accumulated experience, as shown by history.
We look at societies that define marriage as between one man and one woman, and compare its achievements--material and psychological with those of societies diverging from this standard. The original decisions that defined this arrangement may have been arbitrary, "King So&So proclaims..." and so on. But experience has shown it is the best and surest way to widespread contentment.
This is what I mean by my moral argument. If we remove this side of the equation, the foundation of all we have is undercut. We've begun to allow gay partnering to be defined as 'marriage' and entitled it to all the societal obligations and protections accruing to it. As the result of this, we're now obliged to debate the propriety of polygamy. If we concede even one inch of this debate, we'll certainly find ourselves defending our revulsion of child abuse.
"Ye shall know them by their fruit"