The problem here is your failure to study the immediate context of this verse and the overall context and usage of the terms "little children" by Christ and His apostles. This is a regular used metaphorical expression of endearment especially by spiritual leaders toward their followers and it is also a proper description of the spiritual relationship between believers and God.
I will help you in both cases to see the immediate and overall context. First, the overall contextual usage of this termonology as terms of endearment and actual spiritual relationship to God:
Mt 5:45 That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust.
CONTEXT: Those who fit all the other beattitudes - responsible believers
Mt 13:38 The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one
CONTEXT: The proper term to describe the spiritual relationship between true believers and God
Mr 10:24 And the disciples were astonished at his words. But Jesus answereth again, and saith unto them, Children, how hard is it for them that trust in riches to enter into the kingdom of God!
CONTEXT: His apostles
Mt 18:3 And said, Verily I say unto you, Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven.
CONTEXT: The word "as" denotes he is using a simile or comparison. He is speaking to adults and telling them they must become "as" children or a child like submission and faith
Joh 13:33 Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you.
CONTEXT: Addressing His Apostles in upper room discourse
Ga 4:19 My little children, of whom I travail in birth again until Christ be formed in you,
CONTEXT: He is addressing those who had been led astray by false teachers. Literal infants can hardly fit this context.
1Jo 2:1 My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:
CONTEXT: He is addressing those able to READ his letter and who can and do sin. Literal infants can hardly fit this context.
1Jo 3:18 My little children, let us not love in word, neither in tongue; but in deed and in truth.
CONTEXT: He is addressing those who are able to express mature spiritual love for one another. Literal infants can hardly fit this context.
1Jo 2:12 I write unto you, little children, because your sins are forgiven you for his name’s sake.
1Jo 2:18 Little children, it is the last time: and as ye have heard that antichrist shall come, even now are there many antichrists; whereby we know that it is the last time.
1Jo 2:28 And now, little children, abide in him; that, when he shall appear, we may have confidence, and not be ashamed before him at his coming.
1Jo 3:7 Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous.
1Jo 4:4 Ye are of God, little children, and have overcome them: because greater is he that is in you, than he that is in the world.
CONTEXT: In all the above passages the words "little children" is a metaphorical term of affection used to describe ALL His readers regardless of their literal age. This is so obvious that only the blindness of paedobaptism could not see it.
Now for the immediate context of your so-called proof text:
1. In Matthew 13 where he addresses the very same ones - His disciples - he says:
10 And the disciples came, and said unto him, Why speakest thou unto them in parables?
11 He answered and said unto them, Because it is given unto you to know the mysteries of the kingdom of heaven, but to them it is not given.
Mt. 11:25 ¶ At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes.
2. However, let us look more closely at the verses that precede and follow Matthew 11:25 to see how Jesus actually applies this statement:
a. Who is he addressing? Those who had REJECTED Him:
Mt. 11:24 But I say unto you, That it shall be more tolerable for the land of Sodom in the day of judgment, than for thee.
b. Who is he applying this too? All those whom He reveals himself to, who are burdened and laden with sin and who are ABLE to come to Him by faith:
Mt. 11:27 All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him
28 Come unto me, all ye that labour and are heavy laden, and I will give you rest.
29 Take my yoke upon you, and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls.
30 For my yoke is easy, and my burden is light.
The immediate context makes it clear he is addressing ADULTS and this is a rebuke to their unbelief whereas the immediate following context makes it clear he is applying this to ALL who come to him BY FAITH under the burden and yoke of sin as characterized in verses 28-30. Literal infants are not burdened and weary of their sins because they are not even cognant of sin or that they are even sinners. The application is exactly as in Matthew 13:10 and it is obvious to anyone not wearing paedobaptist blinders.
You come to the scriptures wearing the BLINDERS of the traditions of YOUR FATHERS - who were neither inspired by God but were Roman Catholics who never intended to leave Romanism but only make reforms that were neither deep enough or transforming enough.
However, again, notice the language in the following verses which is directed toward ADULT APOSTLES:
Joh 13:33 Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you.
Joh 21:5 Then Jesus saith unto them, Children, have ye any meat? They answered him, No.