Project manager must know the key areas that bring difference to the success of project. These areas can be project planning, budgeting, risks management, ensuring quality of the end product, and leading and motivating the team. Delegating tasks is important for a project manager to spend his time effectively on managing the overall project. Delegation does not help only the project manager to focus more on his work but also helps the other people to grow. When you delegate correctly, you motivate and stretch the person you are delegating to, and you contribute to his or her professional development needs, confidence, and competence. 

Many project managers don’t delegate the tasks because of the fear that they will lose the control on a certain concept or planning. They are self-obsessed people which is totally wrong. Being a project manager, one need to think more broadly and productively. Often team members are perfectly able to perform a task if a chance is given to them with the right amount of support. 
 
It’s always good to consider what you delegate, who you delegate to, and how you delegate.

The old saying about accomplishing a particular job is:

‘If you want the job done right, you have to do it yourself’.

The modern approach can rephrase like:

‘If you want the job done right, you have to delegate it properly’ [1].

Reference:

What is Delegation in Management and How to do it Effectively?