As per the last line in the section of perlsub entitled 'Overriding Built-in Functions':
Finally, some built-ins (e.g. "exists" or "grep") can't be overridden.
The reason being that some builtins cannot be reliably emulated via prototypes. print is one of those functions. You can tell which functions you can indeed override with the prototype function:
Prints nothing. Also, from perldoc -f prototype:
If FUNCTION is a string starting with "CORE::", the rest is taken as a name for Perl builtin. If the builtin is not over-ridable (such as "qw//") or its arguments cannot be expressed by a prototype (such as "system") returns "undef" because the builtin does not really behave like a Perl function.
The specific issue with print is that you can't express the optional filehandle target. (eg: print FH "foo";)
Hope that helps.
** added reasoning behind print not being overrideable.