Love that "may increase." What a ridiculously open-ended, utterly meaningless statement.
Sugar increases the risk of diabetes, not animal fat. Vegans can claim what they want, but there are plenty of actual studies over the past several decades that prove that. There are also plenty of studies showing the health benefits of eating eggs, including <gasp> lowering cholesterol.
Certainly vegetables should comprise a great deal of one's diet, but all these vegan-backed "studies" acting like eating meat is harmful are based on over-indulging, which is bad no matter what you're eating.