Quick answer
Appetite decides taste. The verse observes that the same food is repulsive or wonderful depending entirely on the person's condition.
Read both lines
Both halves use nephesh, a whole living person rather than an immortal part of one, settled in the catalog at 12:10. So this is not about souls in a religious sense; it is about a full man and a starving one meeting the same table.
The NKJV footnotes "loathes" as tramples on, which is stronger and better: the satisfied man does not merely decline the honeycomb, he treads on it. And the second line's claim is the harder one. To real hunger, every bitter thing is sweet, which is a plain statement about what deprivation does to judgment. Chapter 25 warned about too much honey at 25:16 and 25:27; this verse explains the mechanism underneath that warning, and it also explains, without saying so, why a hungry person will accept what a full one would spit out.
Related: Proverbs 25:16 · Proverbs 25:27 · Proverbs 16:26 · Proverbs 12:10
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.