Threads like this really disappoint me. They demonstrate a complete lack of awareness of what composition is all about. Of course 'atonal' (for want of a better word) music is structured. i guess my music's not really featured a strong 'tonal' presence since my early 20s, simply because it's not relevant to anything. There are so many aspects that are part of the compositional landscape: melody & harmony of course, timbre, behaviour, density, dynamic range, forms of interaction & reaction...
Much of the time - & i say this without any intended unkindness - those who find it hard to 'understand' 'atonal' music are simply those you have some way to go before reaching a more mature comprehension of what music is, & - more importantly, what it can be.