Running a fixed blade inverted over your shoulder was most notably a military thing. With all the stuff they carried (pack, multiple belts, ect) there wasn't too many places left one could keep a fixed blade/bayonet. Especially if you wanted it to be easily and quickly accessible with both hands and tight to your body.

Nowadays, you also see a lot of neck knives specifically designed for inverted neck carry.

As many have stated, the biggest downside to this form of carry is loss of knife and/or potential injury. A sheath specifically designed for inverted carry can help to mitigate this.

With that in mind, it's not a carry method I would recommend for everybody. Nor would it be the way I would want to carry my only knife in a survival situation.