The vegan position comes from understanding the reasons for why it's immoral to exploit and kill sentient beings when it's *not necessary.
When we consider why it's not ok to exploit and kill humans, it is reduced to the following: humans are capable of experiencing the life around them and prefer to live, they can feel pain, fear, joy and other emotions that make us not want to experience the negative feelings.
Those experiences are part of what it means to be sentient. Humans and animals are different in many ways, but we have some things in common, including sentience. This means that for the same reasons it's immoral to exploit and kill humans in the context of lack of necessity, it's also immoral to exploit and kill animals in the same context.
The exploitation and killing of animals is not necessary in the 21st century, where we are used to the products that result from exploitation and slaughter of animals, but we have alternatives to all or most of those products. This means that it's immoral to exploit and slaughter animals in the 21st century.
*not necessary = when there are no strong overriding reasons, such as personal survival.