It is true that some studies have linked red meat to an increased risk of heart disease partly due to the saturated fat content. In fact, even chicken can contain as much saturated fat as lean cuts of beef or pork. For instance, a serving of sirloin beef or pork tenderloin has less saturated fat than the same amount of chicken thigh with skin. It is true that poultry such as chicken and turkey is naturally lower in saturated fats but this is only true IF you do not eat the skin. If you want to include red meats in your diet, choose leaner cuts of beef and pork. For beef, choose eye of round, top round roast, top sirloin and flank; for pork, choose tenderloin and loin chops.

Additional Resources:
http://www.mypyramid.gov/pyramid/meat_tips.html