You may want to think about the weather as an anology. Its all atoms as well, still the chaotic interactions between air, water and heat can give rise to rather spectacular phenomena such as tornadoes or snowflakes.
There is no contradiction in that a system may behave fundamentally different than its component parts. A rod of iron typically has a zero, or very low, net charge, whereas it is composed of very manny charged particles for instance. A watch can hold information about the current time, whereas the separate parts do not. A book may hold an interesting story, but the individual letters and words can be rather dull on their own.
Most systems are more than their components, this is particularely true for the human brain.