I find this very inventive. So you know about hashes, you use a hash with the $category being the key yet you insist on using symbolic references? If you already have the hash, why don't you store the array there?

use strict;
use Data::Dumper;

open (FOOD, "<", "food.txt") or die "Can't open food.txt: $^E";
my %categories;
while (<FOOD>) {
    chomp;
    my ($category, $item) = split(/\s+/);
    push(@{$categories{$category}}, $item);
}
print ">$_<\n",Dumper($categories{$_}) for keys %categories;
close FOOD;
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No variables springing into existence and overwriting other stuff willy-nilly, smaller memory footprint and quicker execution.

Symbolic references are (almost) never the right solution. And you do not need to worry why I said almost for a few more years. Believe me!