Why the subtitles are still there even if I've chosen "None" or "No subtitle"?

Learn more about subtitles first. There are usually 3 types of subtitles: built-in, external and fake subtitles.

1. Built-in subtitles are stored on DVD disc. They are saved as standalone files, together with your DVD video files on the DVD disc. You can abandon this type of subtitles when converting DVD to video. 
2. External subtitles don't exist on DVD disc. They are saved separately as files in SRT, ASS, or SSA format. This type of subtitle will appear when playing DVD with some DVD player applications.
3. The fake subtitles are actually not subtitles. They are burned on top of video and thus can't be removed unless you crop the portion where they appear, like you crop a video. 

So, if you select None or No subtitle, and the subtitles are still there, it means the subtitles are fake ones. You have to remove them by cropping video.