There are no end of solutions to make method subs private, the most common one I've seen being some variation on:

sub _private_sub {
   die "_private_sub is private!" unless caller eq __PACKAGE__;
   # private stuff #
}
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The result is that only the package where _private_sub is defined can invoke it as a method. I've used this in the past where I found it sensible, and it has always worked well enough.

While this is a common way to implement private method, it is completely wrong.

If the perl method dispatcher encounters a private method, it should not die, but instead it should skip it an continue the dispatch. Take this pseudo-perl example:

package Foo;

sub bar : public { ... }

package Bar;
use base 'Foo';

sub bar : private { ... }

package Baz;
use base 'Bar';
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Now if under your scheme, this code:

Baz->new->bar;
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would die, but that is not correct, it should succeed and call Foo::bar.

Method dispatching which includes Private/Protected/Public can have many subtle edge cases, some of which are not easily (if at all) solveable with the basic mechanisms provided in perl.