As with humans, our pets can become addicted to food that is unhealthy for them. In fact, research has indicated that for humans during early childhood the brain resets the needs of the body according to what foods are consumed during the formative years. This may lead to cravings of these foods later on in life which can be detrimental to health if the food is not nutritious.
I believe that this is true to a certain degree with our pets, especially cats that are fed grain based diets as kittens and will only settle for similar foods later on in life which overrides their natural instinct to eat meat. In addition to this some foods have additives or are coated with substances which cause animals to be attracted to the food and eat it even though the nutritional value is poor.
Getting pets, especially fussy cats and certain toy breed dogs, to eat new foods that are healthier for them can be a tedious process but it is generally well worth it in the long run as an animal's health improves in leaps and bounds when their body is given the right balance of nutrients from natural ingredients.
A good way to start, which is also useful for pets that have sensitive stomachs and are easily upset by a change in diet, is to convert them gradually over a 2-week period. Start off with 7/8ths old food and 1/8th new food – mix in well, use this for 2 days. For the next 2 days mix ¾'s of the old food with ¼ of the new food. Then for the next 2 days 5/8ths old food and 3/8ths new food......... etc. they often gradually make the change.
Another trick, if they're only keen on biscuits / crumbles, is to crush them up and sprinkle them on the new food. Cats may find the new food more appealing if you add a few drops of soy sauce.
Some animals respond positively if one places a bit of the new food in their mouth, they taste it and decide "OK, this isn't so bad" and then devour the rest.
Stroking, patting and praising them while they eat and hand feeding them to get used to the change is a very handy tactic as they're much more amenable to eating when receiving affection.
When all else fails, try explaining to them that this new food is good for them and will make them feel better. Believe it or not, this has worked in a number of cases!
Some pets end up having their way and won't make the change. For some ill animals, bad eating habits are better than not eating at all, especially if it is in their final days when quality of life is of utmost importance.
With most pets it is worth persevering, as their long-term health will be greatly enhanced by good nutrition.