Can I count every article following extracted meta value?

Use array_count_values() (untested):

<?php
$posts = get_posts( array(
    'numberposts'   => -1, 
    'category_name' => 'bird',
    'order'         => 'ASC',
) );
    
if ( $posts ) {
    foreach( $posts as $post ) {
        $species[] = get_post_meta( $post->ID, 'species1', true );
        $species[] = get_post_meta( $post->ID, 'species2', true );
    } 
}

$species = array_filter( $species );
$counts  = array_count_values( $species );
$species = array_unique( $species );
sort( $species );

foreach ( $species as $specie ) {
    printf( '%s %d ', esc_html( $specie ), $counts[ $specie ] );
}
?>