Starting with CrowdStrike Falcon Sensor version 6.11 on macOS Big Sur, you will need to approve a System Extension before it's fully functional. After CrowdStrike Falcon Sensor installs you will see a prompt to open Security & Privacy in the System Preferences.
Go to the Apple Menu and select System Preferences->Security & Privacy
Click the lock icon in the bottom left if it is not already unlocked. You will be prompted to enter the password for an administrator account. Once unlocked, click the Allow button to allow software from CrowdStrike Inc.
You will be prompted to restart the computer. Do so to enable full functionality. You may also be prompted to allow CrowdStrike Falcon to Filter Network Content. Please click Allow.