Why did Superman have a reversed symbol in some episodes of "Superman: The Animated Series"? I'm not confusing him with Bizarro, the reversed symbol was even in episodes which are not related to Bizarro.
It didn't. As you can see here:
you will notice that these are reversed from the Youtube video you link to. Because the Youtube video you link to was reversed from the original video, to avoid Youtube's Content ID system:
Videos uploaded to YouTube are scanned against a database of files that have been submitted to us by content owners. Copyright owners get to decide what happens when content in a video on YouTube matches a work they own. When this happens, the video gets a Content ID claim.
Videos get uploaded Reversed, Cropped, and Bordered, to avoid being taken down.
There is no way in
Hell Apokolips that DC or the WB would have gone to print and aired an episode where Superman's chest insignia was reversed like that.