Your problem is that you're doing an exact match (with eq) against the alphabetic characters but not the terminal newline. For example, if I type in jaccard, then $metric will be the string "jaccard\n". You should probably chomp the input prior to processing it, e.g.

my $metric = <>;
chomp $metric;
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Example of your code as posted:

Which Metric jaccard or Bleu:jaccard
Which source title or snippet or url:title
bleu not called
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Example after chomping $metric and $source:

Which Metric jaccard or Bleu:jaccard
Which source title or snippet or url:title
in title
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P.S. I also notice you prompt for "Bleu" but test for "bleu": these strings are not equal.

use strict;
use warnings;

print "Which Metric jaccard or Bleu:";
my $metric=<>;
chomp $metric;

print "Which source title or snippet or url:";
my $source=<>;
chomp $source;

if($metric eq "jaccard")
{
    if($source eq "title")
    {
        print "in title";
        system("/usr/bin/perl filecom.pl")
    }
    elsif($source eq "snippet")
    {
        print "in snippet";
        system("/usr/bin/perl searchsnipdup.pl")
    }
    elsif($source eq "url")
    {
        print "in url";
        print"jaccard method not called";
    }
    else
    {
        print "jacccard not called";
    } 
}
elsif($metric eq "bleu")
{
    print "bleu called";
}
else
{
    print "bleu not called";
}
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Have you heard the word "indentation"?