I am a Seventh-Day Adventist Christian and a large portion of us are vegetarian, for multiple reasons, mostly related to health and for me personally, for forgoing the suffering of animals.
The Bible is consistent with a vegetarian diet for many reasons. Yes, there have been examples of men and women of faith eating fish and meat throughout the Bible, including the apostles. God gave the Israelites specific instructions on what meats were healthy and what meats weren't. But this is in the context of a fallen world - which means a world tainted with sin. The ground is cursed (Genesis 3:17-19) and everything is degraded; the nutritional content of plants is likely not as it once was in a perfect world. Before sin, all humans and animals thrived on a vegan diet (Genesis 1:29-30). There was no death. Now, animals must seek the flesh of other animals to maintain nutrition. Dr. Veith, a zoologist, has talked in depth about the scientific evidence for this in his lecture series The Genesis Conflict. Human beings choose to eat meat both because some believe it is important to health, as well including simply to gratify our appetites. Unfortunately, as sin is degrading everything in this world in these last days, meat is becoming less safe to eat. Eating meat, for example, has been linked to increased rates of heart disease and cancer.
God cares a lot about what we put into our bodies. A healthy body is a healthy mind. See Daniel 1:8-13, 1 Corinthians 6:19, 3 John 1:2.
The good news, for those of us who feel the pain of living in a world where innocent animals have to suffer, is that there will be an end to this, and this end is coming soon. In Christ's kingdom, everyone will be vegetarian. There will be no more suffering of animals or of people (Isaiah 65:25). This is how God designed it. The reason he hasn't stopped it a long time ago, is that he loves human beings above all other creatures, because we are made in his image, and he is patiently striving with us until all might have a chance to learn of his love for them, so that we might not perish, but have eternal life.