Amber Collins said "Tell us what the problem is exactly regarding adults having sex with children?"

If you have to ask, you truly are part of the problem, but just to be clear, the problem has everything to do with power dynamics.  How people learn to form and value intimate connections and the effects it has for their entire lives is a vital aspect of healthy human development.  When those in position of authority and influence (or just random adults) sexually gratify themselves with those who are impressionable and vulnerable despite the lasting impacts to those lives, it is a violation of the trust children should expect of the adults in their lives, because those adults are taking something the children don't even understand and therefor can't exchange with mutual consent.  It is due to the devastation these violations have had for so many that these violations need to be prosecuted, and the hard-wired perpetrators need be perpetually monitored.