I have actually seen these verses used on a pro abortion website in an effort to show that God does not value the life of children. They did this because the KJV says little children. Many translations do this the same way giving the idea that these are little children that do not know any better than making fun of an old man. These are actually more as the NIV says and youth. נַעַר na`ar can be translated as young as it is in 1 Chronicles22:5 referring to Solomon or young men as it is referring to Abraham’s Servants in Genesis 22:5 (The NIV translates it as servants here). It also is translated boy in the same verse referring to Issac whom I have discussed before is big and strong enough to carry the wood to build an altar by himself.
Some may say קָטָן Qatan requires the distinction that these are small boys, but it can also be translated lesser (see Genesis 1:16) or of less importance. Regardless it is safe to assume that these boys knew what they were saying which was Go up Baldy. עָלָה `alah should be translated as go up or ascend not go away as some translations incorrectly do.
All this to make the point that these boys were not mauled for making fun of Elisha but because they were mocking God. They did not believe that God had really taken Elijah up in a whirlwind and that is what they are stating here. God punished them for doubting him.