It sounds like this is a problem in psychology and how one person influences another by persuasion. Maybe the following would help. All I am going to do is propose that one can eliminate the human element entirely from discussions of measurement and detection.
We can present quantum theory without the need to mention the word "observer" by providing a model of the kind of physical process which is ordinarily involved in measurement-like interactions. That would be a process involving thermodynamic irreversibility, but not necessarily involving consciousness or reasoning beings. So, for example, the photomultiplier tube "clicks" whether or not anyone hears it click. So then the statement would be not that the act of observation disturbs the experiment, but something more mundane but which does capture correctly what happens: it is the physical interaction between the quantum system and the measuring apparatus which disturbs the quantum system. Of course it does! Why wouldn't it?
With this in hand, the point which makes quantum different from classical is merely that you can't take a limit in which this interaction tends to zero. When the interaction tends to zero, so does the degree to which any information passes from one system to another.
So now I would say to my non-physicist friend that there is not much more to it than that, at least for the practical purpose of everyday calculations and predictions. Of course I am aware that not everyone will be satisfied with my simple model, in that it sweeps under the carpet the exact sense in which a process can be irreversible when quantum theory seems to say that everything is unitary. But for practical purposes the notion of irreversibility is all we need in order to say that a process happened, whether or not any conscious or reasoning being was aware that it happened. Schrodinger's cat is either alive or dead well before anyone takes a peek.