Dr. Zakir Naik (may Allah have mercy on him) explains part of this answer in his book. He writes [with my comments in brackets]:
Question: Why do Muslims slaughter the animal in a ruthless manner by torturing it and slowly and painfully killing it? [my notes: what a horrible lie! Its like asking why do all Muslims kill their mothers?]
Answer: The Islamic method of slaughtering animals, known as Zabiha has been the object of much criticism from a large number of people.
Before I reply to the question, let me relate an incidence about a discussion between a Sikh and a Muslim regarding animal slaughter.
Once a Sikh asked a Muslim, "Why do you slaughter the animal painfully by cutting the throat instead of the way we do with one stroke i.e. jhatka?" The Muslim replied "We are brave and courageous and attack from the front. We are marad ka baccha (macho men), you are cowards and attack from behind". [Dr. Zakir is joking here..]
Jokes apart, one may consider the following points, which prove that the Zabiha method is not only humane but also scientifically the best:
1. Islamic method of slaughtering animal
Zakkaytum is a verb derived from the root word Zakah (to purify). Its infinitive is Tazkiyah which means purification. The Islamic mode of slaughtering an animal requires the following conditions to be met:
a. Animal should be slaughtered with sharp object (knife)
The animal has to be slaughtered with a sharp object (knife) and in a fast way so that the pain of slaughter is minimised.
b. Cut wind pipe, throat and vessels of neck
Zabiha is an Arabic word which means 'slaughtered'. The 'slaughtering' is to be done by cutting the throat, windpipe and the blood vessels in the neck causing the animal's death without cutting the spinal cord.
c. Blood should be drained
The blood has to be drained completely before the head is removed. The purpose is to drain out most of the blood which would serve as a good culture medium for micro organisms. The spinal cord must not be cut because the nerve fibres to the heart could be damaged during the process causing cardiac arrest, stagnating the blood in the blood vessels.
2. Blood is a good medium for germs and bacteria
Blood is a good media of germs, bacteria, toxins, etc. Therefore the Muslim way of slaughtering is more hygienic as most of the blood containing germs, bacteria, toxins, etc. that are the cause of several diseases are eliminated.
3. Meat remains fresh for a longer time
Meat slaughtered by Islamic way remains fresh for a longer time due to deficiency of blood in the meat as compared to other methods of slaughtering.
4. Animal does not feel pain
The swift cutting of vessels of the neck disconnects the flow of blood to the nerve of the brain responsible for pain. Thus the animal does not feel pain. While dying, the animal struggles, writhers, shakes and kicks, not due to pain, but due to the contraction and relaxation of the muscles defecient in blood and due to the flow of blood out of the body.
For answers to more questions relating to Islam from non Muslims, please visit this link: http://www.irf.net/faq.html