Why will iTunes not allow my MP3 files?

If even VLC is balking at playing it, it sounds like it is one of those obscure flavored mp3 files.

MP3 Scan+Repair (including sources): http://triq.net/mac/mp3-validator-mac-os-x

This is an older utility and at some stage OSX will probably stop running it (I still use Mavericks so I can't tell you about High Sierra).

If the above doesn't work you can check tools such as MP3 Trimmer. It has a repair tool. I have a licensed copy so I don't know if the tool is available in the trial mode.

There's a stable of transcoding tools out there you can try instead of iTunes. I dislike using one for this kind of thing because you lose quality with each transcode (the above tools do not transcode). You might have to use one if the mp3 data are truly corrupt/unreadable vs. just some of the packaging. One of my favorite transcoders is XLD - X Lossless Decoder: Lossless audio decoder for Mac OS X - http://tmkk.pv.land.to/xld/index_e.html It is free, powerful, and also used for CD ripping. The interface is a bit weird until you learn that changing settings all has to be done through preferences.

Mp3s are like chocolate bars. Sure, they call it a chocolate bar but they aren't all the same. There's dozens of encoders out there and not all produce the same product. It's rare you encounter one that won't play in iTunes but it is possible. Yours could be damaged. There's an unsupported utility called MP3Scan&Repair that some have found will help in these situations.

What happens when you try playing one?

If it comes down to it even VLC can do transcoding, it's just not set up to be that kind of utility.