Today, secure systems are built by identifying potential vulnerabilities and then adding protections to thwart the associated attacks. Unfortunately, the complexity of today's systems makes it impossible to prove that all attacks are stopped, so clever attackers find a way around even the most carefully designed protections. In this article, we take a sobering look at the state of secure system design, and ask ourselves why the "security arms race" never ends? The answer lies in our inability to develop adequate security verification technologies. We then examine an advanced defensive system in nature - the human immune system - and we discover that it does not remove vulnerabilities, rather it adds offensive measures to protect the body when its vulnerabilities are penetrated We close the article with brief speculation on how the human immune system could inspire more capable secure system designs.