Your mother was right.
I freeze any leftover meat after 1-2 days in the fridge, just so I won’t forget it until it goes off. All this is labeled and it then gets added to whatever is appropriate, sometimes chili, sometimes soup, maybe a stirfry or (for chicken and pork), eggrolls. Soup anywhere can utilize all sorts of leftovers. Before refrigeration, soups and basic sauces were routinely kept simmering on the back of the fire. Ingredients were added as they became available and the entire pot brought to a boil once a day.
We have never been ill from food poisoning with homemade food. Only time we were actually poisoned was from Korean steamtable buffet once when we were out of town for a trade show. I mean fever and bloody stools, vomiting sort of ill. Once. Twenty years ago.
Freezing and boiling kills most pathogens. Wasting food is a sin.