To understand the complexity we need to understand the roles
While these are two different and contentious roles the best case scenario is single point of balance and decision making between the two. To understand the complexity we need to understand that while a Project Managers end role is to for the initiation, planning, execution, and closure of a project they must also define the project, reduce it to a set of manageable tasks, obtain appropriate resources, and build a team to perform the work; in addition to all of this, project managers must be prepared to monitor and mitigate project risks along the way, as well as discover ways to adapt to change, since no project ever seems to go exactly as planned.
On the other hand, business analysts are mainly concerned with the end product and ensuring it meets the requirements and demands of the project's key stakeholders. Business analysts' primary responsibilities are communicating with stakeholders, gathering requirements, and making sense of these requirements in order to ensure that the end products will solve the business problems at hand.
This equation can and does involve a shift from project scope to meet stakeholder requirements, a PM will oppose it such shifts which can potentially effect schedules and costs.
When a project manager and a business analyst are both present on a project team, the project manager can focus their efforts on project schedule, cost, and resource management, and the business analyst can spotlight their time and energy on ensuring accurate requirements management — all critical components of a successful project.