Sacrifice

If they are Americans, ask them what they do on Thanksgiving. If they are English, ask them what they eat at Christmas. And so on. Most cultures have some sort of feast where they eat some kind of meat or animal product, and oftentimes those feasts are associated with religious commemorations.

(Apart from the vegetarians of course!)

Usually people see their own cultural practices as normal and other religious or cultural practices as cruel. 

It is not the people who are suffering from malnutrition or poverty who are saying that it is cruel to sacrifice an animal and share the meat with people who are deprived. The sacrifice is not just to kill the animal and destroy it for the sake of killing or feeding an idol, but rather it is intended to go to good use.

As the Qur'an says, it is not the flesh or the blood of the animal that reaches Allah, but rather it is the piety. In the book 'Ilal al-Shara'i', it is also related that the Prophet (S) said: "This sacrificial offering of the slaughter animal has indeed been established [as part of the pilgrimage rituals] so that your poor may be able to partake of meat, so feed them [with it]."

And, are the people who are criticizing this eating meat? If they are, there is no more discussion to be had. Even if they don't meat, do they have access to a variety of food or nutritional supplements so that they don't suffer from not eating animal products?

Perhaps if the people who are criticizing this spend a year in a situation where they have very limited types of food and are in need of basic protein and nutrition, they would appreciate the gift of meat more. (Especially currently as the world is facing food shortages.)

Similarly, before modern methods of food production, storage, and transportation, which allows for a variety of food, many people relied on having some meat to get proper nutrition, and this was not considered cruel. 

However, it is of course good to look after matters such as the kind treatment of animals, human and sensitive slaughter, and not wasting the meat at hajj, since it was the Sunnah of the Prophet (S) to be kind to animals. These are modern issues that the world is facing due to large numbers of people and the industrialization of animal raising, that are not related to or limited to Islam or Eid al-Adha specifically, but which still should be taken into consideration on a practical level. 

Most people eat animals. In fact all of nature is about eating. If you look outside, all you see is one thing eating another thing, from the birds to the insects to the mice to the cats to the fish and everything else. Lots and lots of eating!

It is really hard to comment on the will of animals. Obviously animals have a survival instinct which makes them dislike being killed. However, most farm animals would not exist at all if people hadn't taken the effort to breed them and raise them.

What can be said is that it is allowed for people to eat animals as long as they are treated and slaughtered in the right way, although some people may choose not to.

The "sacrifice" here is about sacrificing the time, money, and effort it takes to raise an animal (or, if it is purchased, to pay for that) and then giving away a good amount of it. In times where people had very limited food options, or in places where many people don't have access to healthy food, this is a big service to other people. It is one thing to advocate being a vegetarian in a place with many food options and where you can eat a healthy diet without meat or animal products, and a different thing when not eating animals can lead to malnutrition.

(This is as opposed to some older religious traditions where sacrificing an animal for deities or other beings was said to offer things that were useful for them such as blood; the Quran clarifies that God, as pure divinity, does not receive the meat or blood but rather acknowledges the sense of sacrifice.)

Sometimes these questions come up because some people look down on Muslims for being barbaric. However I would point out that in the United States, almost everyone considers it traditional to eat a turkey on Thanksgiving, and eating it requires slaughtering it, and sometimes homeless shelters also serve turkey to those in need, yet it is rare to hear people comment on that or treat it as backwards.