Why should animal fats not be used for cooking?
For one thing, saturated fats tend to have higher melting points, such that at room or body temperatures, they are often solid (though exceptions obviously exist). Therefore, unsaturated fats and oils will be easier to use since they can be poured.

There is also a longstanding, though possibly unjustified, link between saturated fats and oils, and cardiovascular disease. Avoiding saturated fats is supposedly healthier.
Because livestock are more expensive and slower to grow than plants, vegetable or plant oils are easier and faster and cheaper to obtain.
Finally, animal fats often absorb flavour from the animal meat, giving them an unwelcome taste in many contexts. By contrast, vegetable and plant oils either don't absorb anything or the result is attractive pr characteristic in most cooking contexts. So vegetable or plant oils are preferred for versatility and for flavour.