I see two good reasons to split the NSA, neither of which is really discussed by the article:
1.)Computer security is not part of the NSA's mandate. Currently its stated purpose is just spying; it's being pressed into a cybersecurity role because it's the only agency with the talent needed. That means security is secondary to spying. We could change this, but the current system is not optimal from a security point of view.
2.)Perception. The NSA is widely known as a spy agency and that is intimidating. Companies need to trust an entity to seek network defense help from it and an agency that only handled security would probably be viewed as more trustworthy.