Pig fat is considered haram (forbidden) in Islam because the entire pig is considered impure (najis). This prohibition is based on Islamic texts and scholarly consensus.
According to Ibn Hazm (may Allah have mercy on him), "The scholars are unanimously agreed that the meat, fat, marrow, brains and cartilage of dead meat (animals that died without being slaughtered in the prescribed manner), and the meat, fat, marrow, brains and sinews of pigs, are all haram, and all of that is impure (najis)."
Therefore, the prohibition extends beyond just the meat to include all parts of the pig, including its fat. This ruling is part of a comprehensive set of guidelines within Islamic dietary laws regarding what is permissible (halal) and what is forbidden (haram) for Muslims to consume.