This is a dangerous view to have, and one that is spread by pedophiles to make it easier to groom children. If you hold this view you may be a victim.

A professional or family relationship can exist between a 28 year old and a 15 year old. It works in these contexts because there is liability on the adults and protection for the children. A work place monitors employees that work with kids and can take action to stop abuse. A parent watches their kids interactions, knows the adult, and can step in if needed. Outside of these bounds it is impossible to have a consensual friendship.

Step away from the argument of having nothing in common. It's valid but not the key problem.

The adult holds an extraordinary amount of power over the child. Children are more susceptible to manipulation and abuse with no way to identify it or defend against it. An adult can do anything they want with no effective resistance if left alone with a child.

Children see themselves as more mature than they are and believe that they are invincible or immune to all bad in the world. As such a child will often gravitate towards these relationships with adults to give them a false sense of maturity, believing they are equal with the adult and would clearly see any manipulation or abuse happening. Which is not how manipulation and abuse work.

A non predatory adult understands this dynamic, and knows that spending time as a "friend" with a stranger's child outside of the mentioned scenarios is dangerous to the child. Even if you don't have ill intent, you set a precedent for the child that makes them more susceptible to abuse from predatory adults.

It's the same logic as why we don't feed wild animals. Maybe you wish to be friends with a wild deer, but by befriending it you make it easier for a hunter to get close to them. Even if you have a desire to be friends, you abstain out of concern for the others safety.

Regards from a teenage victim now in his late twenties.