You are building your array and iterating over it at each iteration of the outer Loop. Think about what happens.

First iteration of the outer loop

$get_year becomes array('2012') and you iterate over it echoing “2012”.

Second iteration

$get_year becomes array('2012',2013') and you iterate over it echoing “2012” and “2013”.

Do you see what happened? You have echoed the same data twice. You are echoing the partially constructed $get_year array. The more posts you have the bigger the problem will become and I would not be surprised if it crashed the browser eventually.

Pull that foreach out of the other loop so that you only iterate over it once– after it is has been completely constructed.

$loop = new WP_Query($args);
while($loop->have_posts()) {
  $loop->the_post(); 
  $get_year[] = get_the_time('Y'); 
}
foreach($get_year as $year) {
  echo $year;
}
wp_reset_postdata();