When people make the decision to diet, they try to avoid large amounts of calories or carbs, but never think about avoiding fats (meat, dairy, eggs, and oil.) In fact, I hear more often to avoid carbohydrates and eat more fats. Most people want to keep eating meat and dairy (fat), so they try to starve themselves of all other foods so they can continue to lose weight. Of course you can lose weight very fast by reducing your calorie intake, which is why people turn to that technique, especially men because they want meat. However it isn't realistic to believe you will maintain your ideal weight by reducing your calories and carbs. You'll binge out if you reduce calories and carbs for a long period of time.
Veganism makes more sense because you can eat large quantities of calories and carbohydrates from veggies, fruit, grains, and beans which will make you feel full consistently, while giving you large amounts of vitamins that animal products lack. Why don't you eat a LOT of calories and carbohydrates from fruit and vegetable sources so you can lose weight faster and get the most nutrition?
If you're concerned about vitamins on a vegan diet, I assure you that you can get the recommended amount of protein, calcium, vitamin D, and b12 from your calories through these plant-based sources:
Protein: Fruits (bananas), vegetables, Beans, nuts, seeds, oats, quinoa, soy products
Calcium: leafy greens, broccoli, cabbage, figs, dates, oranges, fortified soy products (soy milk has 50% more calcium than cow's milk)
Vitamin D: Mushrooms, sunshine, and fortified soy milk
B12: mushrooms, greens, and fortified soy or almond milk (or other Silk products)
Below I have listed the most common ways to replace the unhealthiest of fats:
Meat (for protein and in baking): Beans, Quinoa, Nuts, Rice, and Oats
Dairy (for drinking and in baking): Water, soy(bean) milk, rice milk, coconut milk, almond milk. Store bought soymilk is fortified with 50% more calcium than cow's milk. It is also fortified with essential daily vitamins.
Eggs (in baking): Pumpkin (puree), applesauce, mashed potatoes (for hearty meals), mashed bananas, non-dairy yogurt, and flax meal + water. You can also purchase Ener-G Egg replacer (which contains potato starch and tapioca starch to bind baked goods).
Oil (in baking): Applesauce, non-dairy yogurt
Oil (for frying): Slowly add water or vegetable broth/stock to a heated pan with veggies you're frying.
Sugar: mashed bananas, maple syrup (pure), molasses, or dates (pureed)
Hope this was helpful~