when ripping a disk, subtitles are usually included in an image-based format (e.g. VOBsub for DVDs or PGS for Blu-Rays). This is basically a sequence of pictures where each picture represents one subtitle – each of them with a timecode when to appear/disappear.
There’s a lot of clients which cannot deal with those picture based subtitles. Also… formats like e.g. mp4/m4v don’t support embedding them.
Therefore, many apps interpret “including” a subtitle as “burning them in” – what this does is basically it merges the subtitle picture with the video and outputs 1 combined video. This is usually called
hard subtitles (because they’re hard-coded and cannot be switched off).
To allow turning subtitle on/off, you need to get them into the movie container as a separate stream (same as video or audio tracks). This is called
Option 1: use a container which accepts image-based subtitles (e.g. MKV) – assuming your client can deal with them. You can do this e.g. with MakeMKV (which will directly create a soft subtitle while ripping it) or MKVToolNix (which can mux the subtitle file into an existing MKV file)
Option 2: get a text-based version of the subtitles and mux it into your existing video (MKV but also MP4/M4V, others) – many clients can deal with those. You can use a service such as SubZero or subtitles.org to download the right files for your movie… alternatively you can use an app to convert the image-based original subtitles into plain text (like a scanning app which recognizes the letters) – there’s a number of apps which can do this with varying quality results. On my Mac I used to use Subler which automatically converts the image based subtitles to text based ones (SRT) when adding them to a movie.