The phrase "a false sense" means a belief or understanding that is not accurate, real or true. It refers to something that appears to be correct but in reality it's not. A person may have a false sense of security if they think everything is under control when it actually isn't. Similarly, someone might have a false sense of superiority over others due to their wealth, status or achievements. In essence, the phrase "a false sense" implies that something seems right but in reality it's not, and can lead to misguided decisions or actions based on this incorrect perception.