Most pets have 1-3 foods that either do not heal them, do not overwrite the stat buff of a food they are replacing (ie pet using bark for a str buff, then you put on say fiber for a vit buff and nothing happens), and/or provide no stat buff like previously or their food table shows.
Look at unappetizing fish for a greater bear. Should add +14 str, and heal some. It will add the +14% str only if the bear currently has no food boost and it does not heal any. If the bear has a buff from a diff food, like honey, the unappetizing fish doesnt overwrite the boost from honey