Arguing from evolution or physiology (sharp teeth, flat teeth, etc.) is a poor argument. Not only are there many obvious counter-examples (Red Panda eat mainly bamboo), but the "natural" diet tells us nothing about which diet is optimal. Consider the pros and cons:
For pros, while in "the wild" eating meat may be advantageous as a source of nutrients, modern humans have access to highly nutritious legumes, grains, and veggies (including the ability to cook to increase digestibility) all year. We also have B-12 supplements. This makes the benefits of meat in the modern world virtually non-existent.
In terms of cons, modern humans live much longer (as do domesticated animals) and have less active lifestyles, meaning what may have been a non-issue in "the wild" like carcinogens or substances that increase cardiovascular risk becomes much more concerning in the modern world with people regularly living into 60s, 70s etc.
We don't have to worry about starving anymore due to a bad hunt, or being eaten ourselves by saber tooth cats, but with increasing longevity comes risk factors that have never been very meaningful in our evolutionary history. When you only lived into your 40s and were running around all the time cancer and heart disease just were'n't really issues that your physiology had to adapt to.
In a civilized/domesticated setting, I'd argue a vegan diet is better even for animals like dogs which "in the wild" ate far more meat than our near relatives (chimps, etc. who eat only around 10% of calories from animal products), and while we have limited data on that, existing anecdotes seem to suggest dogs live longer on plant based diets too.
When it comes to humans, there are few large vegan populations to study. Remember that B-12 was only discovered in the late 1940s as the missing nutrient that once made strict veganism impossible. Now that we have supplements, people can be vegan. But because of this there are no traditional vegan populations.
However, there are many populations of low-meat eaters. If you look at the longest lived people, from the Mediterranean diet to the Okinawan diet, you see a trend of less animal product consumption. So moving in the plant-based direction is undoubtedly superior from a health perspective.
We also have some limited evidence from modern vegans that suggests vegan populations live longer.
It's hard to say if there is very much difference in eating very little meat vs. no meat. The fact is that only a small amount of something isn't going to show up in the mortality data (like a population that smoked 1 cigarette a week isn't likely going to have a visible impact on mortality).
But we can see the trends and we know at least that people should not be eating much animal product, so you have nothing to lose by reducing your meat consumption. Just make sure you replace it with nutritious foods like beans and legumes, and take a vitamin.
In terms of hunger, that probably has to do with calorie intake. You need to try out some recipes with more healthy plant-based fats and proteins to keep you full and nourished. Just take your time transitioning and reducing your animal product consumption step by step, learning how to replace things as you go. Sometimes going too fast can result in rebound because we're left not knowing what to eat. There's a little learning curve there.
I hope that helps answer your questions.
