And to put a fine point on it, the age of consent in New York is 17 and is 16 in New Jersey.
So I think the focus on "child" is not only misplaced, but untrue. Rape is the real issue, so that's the real thing to focus on.
The argument is flawed because we generally tolerate power differences in relationships: men and women (institutional power), certain cases of coworkers of different ranks, an able-bodied person with a disabled person, a depressed person with a mentally healthy person, a suicidal person with a happy person, etc.
There are also a lot of adults who vary, due to personal characteristics or experiences with relationships (or lack thereof) who are far more easily snared into a relationship; the average 17 year old has had many more relationships than I have as a 25 year old, and sexual ones too, usually with peers. If anything, I'm the naive one who would fall into a very convincing snare with an older man.