I wonder where the idea comes from that classical music is only (or mainly) enjoyed by adults? I am maybe older than many of the people on this site and yes, I love classical music; but I also loved it when I was a kid, and I know many adults who do not particularly enjoy it. And remember there are many sub-categories within what we loosely call "classical" music. Personally I don't enjoy them all equally. For example I have a great fondness for baroque, contrapuntal music, in particular that of J S Bach; I also love music of the strictly 'classical' age, but I do not care much for the Romantic composers such as Chopin. As for 20th century music - some is great but some (for example the twelve-tone stuff by composers such as Schoenberg) sounds plain ugly to my ear!
I think we often tend to respond most to the type of music that we heard around us when we here young. So if you grew up in a family that listened mostly to classical music, that is the sort of music you learn to appreciate best. Other families may have introduced you more to jazz, or country, or rock music, whatever.
For me, the wonderful thing about classical music is its complexity, and depth. Classical compositions can be long enough to explore many themes and moods, and they invite the listener to contribute to the experience, because your own emotions and reactions enhance and change how you feel about what you hear. So your experience of hearing even the same piece of music can change from one occasion to the next. This is perhaps why classical music 'lasts'; we can still listen to music that is hundreds of years old with enjoyment. A composition is not expected to be popular just for a matter of weeks before it fades from memory.
I think this idea that the listener contributes to the experience of music is common to all great art; music, graphic art, sculpture, literature, poetry .... the greatest examples of all of these invite their audience/viewers/readers to form their own experience of what they see, so that everyone in a way hears and sees something personal and different.
These are some of the reasons I love classical music and would find life diminished without it! Persononally I dont respond much to pop /rock/country music, so perhaps I could ask, as the converse to this thread, what is it about these types of music that other people - maybe younger people but not exclusively - find so wonderful?
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'All men dream, but not equally. Those who dream by night .... wake in the day to find that it was vanity:but the dreamers of the day are dangerous men, for they may act their dream with open eyes, to make it possible' (T.E.Lawrence)