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Rooting is the method that allows users to gain privileged control within Android's subsystem. This process involves obtaining root access to the Android operating system, which is similar to jailbreaking in iOS devices. By rooting an Android device, users can bypass restrictions set by the manufacturer and gain access to the root file system, enabling them to modify system files or install applications that require elevated permissions.

Rooting is significant in the context of ethical hacking as it allows security professionals to perform advanced security assessments and penetration testing. This level of access can help in identifying vulnerabilities that are not usually accessible in standard operating conditions.

On the other hand, the other methods mentioned don't provide the same level of access to the Android operating system. Jailbreaking specifically refers to bypassing restrictions on iOS devices, proxying involves routing network traffic through another server (which does not grant control of the device), and firewalling is a security mechanism that controls incoming and outgoing network traffic based on predetermined security rules. None of these methods confer root privileges on Android devices, making rooting the only correct answer in this context.