What are the benefits of making a DI container more than a factory?

There is a lot of discussion about this, but nobody seems to really answer the question.

I am currently considering using a Symfony 2 service container . The more I look at it, the more it looks like I could do the same with a factory service. Consider the following example:

services.yml

services:
    my_mailer:
        class:        Acme\Mailer
        arguments:    [sendmail]
    newsletter_manager:
        class:     Acme\Newsletter\NewsletterManager
        arguments: [@my_mailer]

      

        
        
        
      

    

Now, to get the news manager, I do something like:

// this has been configured with the above yml file
$serviceContainer = new ServiceContainer();
$newsletterManager = $serviceContainer->get("newsletter_manager");

      

        
        
        
      

    

However, consider the following factory style code:

class ServiceContainer
{
    public function getMyMailer()
    {
        return new Acme\Mailer("sendmail");
    }

    public function getNewsletterManager()
    {
        return new Acme\Newsletter\NewsletterManager($this->getMyMailer());
    }
}

      

        
        
        
      

    

And then using it:

$serviceContainer = new ServiceContainer();
$newsletterManager = $serviceContainer->getNewsletterManager();

      

        
        
        
      

    

Is there something I am missing here? Because I really don't see the benefit of using a DI container if a factory can do all of this for me.

I've heard that using factories makes your code "depend on a factory". I either don't understand this argument or the person arguing with factories is confused. Only the top level class (composition root) will have a reference to the factory, as it is, the only one to have a reference to the DI container.