There might be some confusion here, because killing animals in the church would probably not be done by most Christians.
If, however, you mean "why to Christians kill and eat animals, in general?" then I can answer that.
Christianity inherited its beliefs about food and animals from Judaism. Animals are perceived differently to Christians. They are not equal with humans and their lives are precious, but not as valuable as human lives. From the creation story in Genesis, Christians are taught that animals, and even all of Creation, is under man's dominion and stewardship. Consider this comment below for some further thoughts.
Further, consuming animal meat is a large part of the culture Christians inherited from Judaism. There are Christians that advocate vegetarianism, but they are very few in number. Most Christians think that neither is a sin, to eat or not eat animal meat, so if you personally do not want to eat you do not have to, but you should also not judge what others eat. Consider 1 Corinthians 10:31 (NIV):
So whether you eat or drink or whatever you do, do it all for the glory of God.
Most Christians today interpret this as it being acceptable to eat or drink whatever you like so long as you glorify God when you do (i.e. avoid drunkenness and gluttony).
Reference: What does the Bible say about vegetarian diets?