Most guys are suprised there are very negative aspects of animal protein. How could this be when you have so many diets such as Atkins, South Beach, Low Carb and so on that are based on an abundance of meat and dairy? Furthermore, haven't humans been eating meat since the dawn of antiquity?
I can only tell you this: animal protein has some very positive AND some very negative qualities. It is almost always a mistake to ignore or hide the research and such is the case with animal protein. I eat between a half dozen and a dozen egg whites every day, but I know there are potential issues there.
Consider these problems with animal protein that the research has uncovered:
1. Lower Testosterone. There are a couple of studies that show higher protein levels mean lower testosterone. For example, one study of seven healthy men found that those with higher protein levels had 26% lower testosterone levels.  The key according to this study was the protein to carbohydrate ratio. (Fat and calories were held constant.) For more information, read my link on Testosterone and Diet.
2. Cortisol. This same study found that high protein meant higher cortisol as well.  Of course, this is a very undesireable situation - lower testosterone and higher cortisol - since lower testosterone is assiated with diabetes and heart disease and higher cortisol with neuron damage, muscle loss, visceral fat deposition ("beer gut") and many other nasty anti-male qualities. Read my link on Cortisol and Stress for more details.
3. Bone Loss. There is some evidence that higher protein diets can lead to bone thinning and eventually osteoporosis (in some cases). For example, in many of the supercultures that eat little dairy and almost no meat, osteoporosis is much less common. According to conventional medical wisdom, these third world cultures should be rife with osteoporosis and hip fractures due to low calcium levels, but, in fact, the opposite is true. Furthermore, several studies on the Eskimos have shown that they have accelerated bone loss and one of the key features of their diet is high animal protein.  One reason that experts speculate may be behind this phenomenon is that protein adds a tiny acidic load on the blood stream and the body, to compensate, pulls calcium from the bones to neutralize it. However, in fairness, the Eskimos have a low calcium diet and so that could play a role as well.  NOTE: This has also been shown to be an issue for post-menopausal women, so you might want to tell your woman if it applies.  Interestingly enough, significant bone loss was experienced for women consuming high levels of beef, chicken and vegetarian protein.
4. IGF-1. Many studies have shown that casein, the primary milk protein, increases IGF-1 and inflammation. This is something I discuss in more detail in my link on The Pros and Cons of IGF-1, but suffice it to say this likely increases your risk of cancer and other problems.
5. Homocysteine. Protein has been shown in several studes to raise homocysteine levels, a significant risk factor for heart disease. For example, one study of healthy pre-middle-aged males found that a higher protein diet (21% of calories) lead to elevated homocysteine levels when compared to a lower protein diet.  There is some evidence that exercise can lower homocysteine levels, but clearly this is a potential risk.
6. Decreased Immunity. Amino acids have powerful effects on the body, including our immune systems. One surprising property of protein, that most bodybuilders and athletes do not realize, is that the research shows that in many cases it can negatively effect our ability to fend off infections, parasites and autoimmune disorders. This is a big subject, which I cover in my link on Protein and Immunity.
7. Gout and Urate Kidney Stones. Increased uric acid levels are an outgrowth of eating purine-rich foods such as red meat and sea food. One 12-year study of men found a 50% increase in gout from eating these high-protein foods.  High protein diets are also associated with an increased risk of the less common urate kidney stones. However, high uric levels may increase formation of the much more common oxalate kidney stones. Both gout and kidney stones are very painful conditions. Keep in mind that the erection-killing Metabolic Syndrome and insulin resistance are also associated strongly with elevated uric acid levels putting many modern, urban dwellers at risk for these issues.
8. Increased Systemic Inflammation. Researchers found that a high protein diet increased the inflammatory markers of "fibrinogen, Lp (a), and C-RP increased by an average of 14%, 106%, and 61% respectively."  And we all know that elevated inflammation is the root of all evil, a root cause of heart disease, erectile dysfunction, autoimmune disease and cancer.
9. Lower DHT. DHT is important to libido and other functions of male health, so it is of some concern that researchers found that increasing the protein/carbohydrate ratio lowered DHT levels. For more information, see my page on How To Increase DHT Naturally.
MYTH: Higher protein diets have not been shown to affect kidney function. 
So why do I consume a lot of animal protein in the form of egg whites? Well, egg whites have no Saturated Fat, so I avoid all the problems associated with saturated fat consumption. (See my page on The Potential Dangers of Saturated Fat for more information. Furthermore, egg whites are part of the Ornish Diet, which has a strong research track record. (Well, maybe not as many as I consume!)
Finally, I lift weights and megadose on Vitamin C. These two things can potentially - and I emphasize potentially - protect me from 1-3 above. Lifting weight has been shown in several studies to raise baseline testosterone and, of course, any weight bearing exercise is strongly protective of bone tissue. Finally, megadosing on Vitamin C has been shown to lower cortisol and so I am counting on this to compensate.
1) Life Sci, 1987 May 4, 40(18):1761-8, "Diet-hormone interactions: protein/carbohydrate ratio alters reciprocally the plasma levels of testosterone and cortisol and their respective binding globulins in man"
2) Am J Clin Nutr, 2003, 78:584S-592, "Bone mineral content of North Alaskan Eskimos"
3) Acta Medica Scandinavica, Jan/Dec 1983, 214(2):99 101, "Serum Calcium in Greenland Eskimos"
4) J Gerontol A Biol Sci Med Sci, 2010, "Protein Intake, Weight Loss, and Bone Mineral Density in Postmenopausal Women"
5) J Amer Dietetic Assoc, 2007, 107:1404-1408
6) American Journal of Clinical Nutrition, Sep 2005, 82(3):%53-558, "A high-protein diet increases postprandial but not fasting plasma total homocysteine concentrations: a dietary controlled, crossover trial in healthy volunteers"
7) N Engl J Med 2004; 350:1093-1103, "Purine-Rich Foods, Dairy and Protein Intake, and the Risk of Gout in Men"
8) Angiology, 2000 Oct, 51(10):817-26, "The effect of high-protein diets on coronary blood flow"