Why is my video on youtube removed for copyright infringement and not for other users with same video?

I uploaded a clip from a film on youtube with the name and everything and it got removed for copyright infringement. Yet if I look up the same film title, I find that other users have clips from the film without any mention of the "I don't own this clip or this clip belongs to Universal Studios" or whatever. How do I upload my clips the way these folks do it and not get hled?