These Little Ones

People believe that these verses apply to all children. I hear it all the time. Do you also believe these apply to all children?

“Whoever causes one of these little ones who believe in Me to sin, it would be better for him if a millstone were hung around his neck, and he were drowned in the depth of the sea.  Woe to the world because of offenses! For offenses must come, but woe to that man by whom the offense comes! Take heed that you do not despise one of these little ones, for I say to you that in heaven their angels always see the face of My Father who is in heaven.  For the Son of Man has come to save that which was lost. What do you think? If a man has a hundred sheep, and one of them goes astray, does he not leave the ninety-nine and go to the mountains to seek the one that is straying?  And if he should find it, assuredly, I say to you, he rejoices more over that sheep than over the ninety-nine that did not go astray.  Even so it is not the will of your Father who is in heaven that one of these little ones should perish."
Matthew 18:6-7, 10-14 NKJV

That is an absolutely erroneous reading of this Scripture. There are important parts that one must miss in order to think these verses apply to all children.

First off Jesus defines who the "children" and "little" ones are. It is the "converted" ones.

Then Jesus called a little child to Him, set him in the midst of them, and said, “Assuredly, I say to you, unless you are CONVERTED and BECOME AS LITTLE CHILDREN, you will by no means enter the kingdom of heaven.  Therefore whoever humbles himself AS THIS LITTLE CHILD is the greatest in the kingdom of heaven.  Whoever receives one little child like this IN MY NAME RECEIVES ME. Whoever causes one of these little ones WHO BELIEVE IN ME to sin, it would be better for him if a millstone were hung around his neck, and he were drowned in the depth of the sea.  Woe to the world because of offenses! For offenses must come, but woe to that man by whom the offense comes!
Matthew 18:2-7 NKJV

These Scriptures further verify the same, because IF He were speaking of every child born, EVERYONE will be saved since not a single "sheep" will be lost.

“Take heed that you do not despise one of these little ones, for I say to you that in heaven their angels always see the face of My Father who is in heaven.  For the Son of Man has come to save that which was lost. What do you think? If a man has a hundred sheep, and one of them goes astray, does he not leave the ninety-nine and go to the mountains to seek the one that is straying?  And if he should find it, assuredly, I say to you, he rejoices more over that sheep than over the ninety-nine that did not go astray.  Even so it is not the will of your Father who is in heaven that one of these little ones should perish."
Matthew 18:10-14 NKJV