A more helpful answer for you:
Why do you see them on your news feed? - It's just one of the elements of social media and just how it works..
Can you stop seeing their posts on your news feed? - Yes you can and here is how - Click the drop-down menu arrow at the top right of any post in your News Feed and choose Hide post to see fewer posts like it in the future. Alternatively, click Unfollow to stop seeing all updates from the friend in question, without actually unfriending them completely