There are a few ways to do this.
One option would be a simple if check in the template:
<p>Article detail:</p>
<h2>{{$article->title}}</h2>
<p>{{$article->content}}</p>
<h4>The other articles of this user:</h4>
@foreach ($articles as $otherArticle)
@if($article->id !== $otherArticle->id)
<p>{{$article->title}}</p>
@endif
@endforeach
Another, perhaps better option would be to exclude the main article from the data in the controller:
function showArticle(Article $article)
{
$otherArticles = $article->user->articles->filter(
function($otherArticle) use($article) {
return $otherArticle->id !== $article->id;
});
return view('someview')
->with('article', $article)
->with('otherArticles', $otherArticles);
}