CoreOS : Read-only file system
In CoreOS the /usr partition is read-only by design, so /usr/local/bin/ will be read-only too (unless you mount another disk there). This allows for the auto-updating CoreOS uses to keep the OS current. You can see the partition layout here.
You can install your binaries, etc. in another partition. I usually use /opt/ for this purpose. You can either mount another disk on /opt/ or rely on the fact that / is read-write, depending on your use case, size of files installed, etc.