That statement is known as Brooks’s Law, and it was coined by the renowned computer scientist and software engineer Frederick P. Brooks. Concretely, the original statement found in his 1975 classic The Mythical Man-Month is “adding manpower to a late software project makes it later”. Basically, the idea is that adding more analysts, designers or programmers to a project running behind the original schedule will delay it even more.
Broadly speaking, the rationale of Brooks’s law is related to knowledge management. First, when new personnel is added to the project, some resources have to be diverted into training or informing the newcomers about the project’s status, vision and philosophy. That will delay the project. Further, when the number of people participating in a project increases, so does the number of communication paths. Thereby, more resources (including time) are required in order to distribute the information. Regarding this point, you may be interested in reading my entry on “Knowledge Sharing” in Software Design, Trials and Errors.