Internet attacks and vulnerabilities are increasingly held secret and sold to the highest bidder. Unfortunately, this encourages developers to hide back doors and seel them on the open (black/grey) market. This compromises the security of the Internet at large, and our personal security as well.
Open-source software provides the ability for many eyes to publicly vet the security of software, particularly when software patch commits are audited by more than one person. While open-source software may not solve the problem, the open philosophy provides a community for public code review. Certainly a closed-source backdoor would be more difficult to detect than an open-source backdoor—though I am sure others may debate my argument.
I encourage you to read Bruce Schneier’s most recent Crypto Gram for further discussion on this topic: