Veganism is a philosophy and lifestyle that rejects and seeks to avoid all forms of animal cruelty and exploitation, as far as possible and practicable. Its main practical application is following a strictly plant-based diet.
I was originally against the idea of veganism. I started doing research in order to be able to properly argue against it, but what I found instead is that arguments for veganism were stronger and made more sense. I felt the moral obligation to go vegan, and eventually made the change in 2012.
I think there are 3 main points that lead to veganism:
Animals have feelings
Looking at a bunch of cows in a farm, one might think that they are barely more than biological robots, following their instincts without agency. But one would think the same of humans if looking at footage of a crowded city. We don't look different than ants.
It's only when looking at individuals with enough attention that we can see their individuality. No one who ever had a dog or a cat as a pet would doubt that they have feelings or distinct personalities. Some are more aggressive, some more playful, some more energetic, some like fetching a ball, others prefer belly rubs. They are undoubtedly conscious beings that can feel joy or pain and desire for a happy life.
Cows, pigs and chickens are no different. If you had any of them as a pet you would see no substantial difference with a dog or a cat. Pigs are actually more intelligent than a dog, and even 3 years-old human children.
Most people feel outraged when they hear about the Chinese Yulin Festival, were they boil dogs alive to eat, yet think it's OK to do the same to other animal species, the ones that aren't usually used as pets. This is a cognitive dissonance.
Animal exploitation is cruel
Animal exploitation industries are brutal and cruel. Male chicks are often blended alive soon after birth. Pigs and chickens are mutilated without anesthesia. Laying hens lay eggs to exhaustion and are then killed. Most of them are forced to live in either cages where they can barely move, or crowded in an industrial unit, forced to grow at an abnormaly fast rate and then sent to a horrible and frightening death at a slaughterhouse.
These are just a few of the horrors industry-farm animals endure. Even the ones best taken care of at more traditional farms get a short life and a brutal death. Future humans will look at our practices in horror, judging them at the level of slavery.
There is no need to consume animal products
If we had the need to consume animal products to survive, an argument could still be made that it is a necessary evil, but this isn't the case.
A vegan diet is not only perfectly adequate, but arguably healthier than an omnivorous diet, as meat is linked to a bunch of serious diseases, including cancer.
Following a vegan diet is also extremely easily nowadays, with even plat-based substitutes of meat products like hamburgers available at most super markets (at least in first-world countries).
The bottom line is this: You can choose between two comparable options, one of which causes more suffering than the other. What kind of person would choose that one? Not the kind of person I want to be.
You might think you have further objections, like "plants are living beings too" or "we can't feed the world with just plants". Refer to this video to have them refuted.