The usual disclaimer - this is the Young-Earth Creationist, Biblical Literal view, which is not the only view out there.
Many Creationists, including Ken Ham, Kent Hovind, and others believe and teach that the relationship between man and animals was changed directly by God after the Flood.
Before the Flood, man was vegetarian only:
Genesis 1:29-30 (KJV)
29 And God said, “See, I have given you every
herb that yields seed which is on the face of all the earth, and every
tree whose fruit yields seed; to you it shall be for food.
30 Also, to every beast of the earth, to every bird of the air, and to
everything that creeps on the earth, in which there is life, I have
given every green herb for food”; and it was so.
but after the Flood, man became omnivores.
Genesis 3: 1-3 (KJV)
1 And God blessed Noah and his sons, and said unto them, Be fruitful,
and multiply, and replenish the earth.
2 And the fear of you and the dread of you shall be upon every beast
of the earth, and upon every fowl of the air, upon all that moveth
upon the earth, and upon all the fishes of the sea; into your hand are
3 Every moving thing that liveth shall be meat for you; even as the
green herb have I given you all things.
As to when the animals became dangerous to each other, the Bible doesn't specify. Some suppose it was after the banishment from the Garden of Eden, some speculate that it was at the same time the relationship between man and animals changed in Genesis 3. But Scripture doesn't say for sure.
Answers in Genesis interprets Genesis 1:29-30 as stating that man and animals were all vegetarian, which does appear to be the case from a plain literal reading of the verses. Kent Hovind claims the same thing. So they would naturally assume that animals became meat-eaters after the Flood as well.