Because == evaluates 'a' in numeric context. eq is used for alpha comparisons, but it will never match because $select still has a newline character (\n) appended from the input.

#!/usr/bin/perl 

use warnings;
use strict;

print "what is your name: ";
chomp( my $name = <STDIN> );
print "hello $name\n";

print "select letter\n";
chomp( my $select = <STDIN> );

if ($select eq 'a'){
    print "good choice\n";
}
else {
    print "bad choice\n";
}
[download]

Outputs:

what is your name: steve
hello steve
select letter
a
good choice
[download]