Read more problem

Hello!
I’m kind of a newbee to this PHP wordpress thing but I managed to customize the theme Modularity Lite for my wordpress a bit already.

The problem is, when you see my index page (https://www.mc-arun.com/draaitdoor) you see my most recent post listed.
I chose to cut in my posts by adding the tag MORE in the editor, as you all know I guess..

But, when I add the MORE tag in my posts, not every post has the read_more text underneath it (in my case ‘Lees het hele artikel’, Dutch for Read the whole article).

I already edited things in the post_template.php file following instructions at https://codex.www.ads-software.com/Customizing_the_Read_More

But still, not everywhere is my Read More Text shown..

In Archive (per month) it’s shown though..