Answer: The Word of God lets us know that animals have a soul, but not a spirit. The soul is the seat of the emotions and appetites, whereas the spirit is the seat of one’s intelligence. 1 Corinthians 2:11 states,
"For what man knoweth the things of a man, save the SPIRIT of man, which is in him?"
In Job 32:8 we are told,
"But there is a SPIRIT in man: and the inspiration of the Almighty giveth them UNDERSTANDING."
Now, notice Psalm 32:9,
"Be ye not as the horse, or as the mule, which have NO UNDERSTANDING (i.e. no spirit): whose mouth must be held in with bit and bridle..."
Animals act on their emotions and appetites by instinct. Upon death, the body and soul of an animal cease to exist. By this I do not mean that animals have no value, and we should not be considerate of them. To the contrary, since this life is all an animal has, God wants us to be kind to animals. Proverbs 12:10 tells us," A righteous man regardeth the life of his beast."
God wanted mankind to live eternally so He could have fellowship with thinking beings. Man’s sin made that impossible, separating us from God. Therefore, Jesus Christ came to this Earth, died on the Cross and was resurrected to pay for our sins. Death for an animal is the end. Death of a person is just the beginning of their eternal life, either in Heaven or in Hell.
"Verily, verily, I say unto you, He that heareth my word, and BELIEVETH on him that sent me, hath EVERLASTING LIFE, and shall not come into condemnation (Hell); but is passed from death unto life."- John 5:24