Have you ever tried to hammer a nail with the handle of a screwdriver? It doesn't take long to realize it's not going to work. It takes even less time to understand that the time you invest in buying a hammer will be gained many times over when you need to hammer nails.
Having the right tools to do a job is crucial, regardless of the job you're doing.
When managing projects, using an Excel sheet or a Word document or even the very simple "emailing a task list to everyone" will only make your project difficult, or even impossible to manage. Manual project management forces the project manager to remember a lot of things that software solutions can automate easily.
For example, if you're doing manual project management, you'll need to remember to remind you team when tasks are getting close to their due dates. Project management systems like AceProject will do that automatically. You'll also need to follow up with your team if their tasks are late – another task that can be automated with a project management system. At the end of the week or month, you'll need to key in all the new data in your Excel/Word/Email document, and manually produce reports – which, of course, can be automated with project management tools.
It all comes down to how much time you're willing to invest in learning a new tool, compared to how much time you're willing to wasted doing things manually.