Baptism: Symbol or Requirement

Baptism, as a whole, in this day in time, is defined and practiced many ways. In the days before Christ, and even John the Baptist, baptism was a ritual practiced by many diverse people for their own reasons.
"Baptism was a rite characteristic of John the Baptist's ministry (Mark 1:4, 11:30; Luke 7:29), and was imposed upon converts from the beginning of the Christian church (Acts 2:38-41, 19:3-5). Analogies to this use of water in religious ceremonies are found in the Eleusinian Mysteries in Greece, certain Babylonian religious rituals, and Jewish priestly ordinances (Num 19:7). Just prior to the Christian era proselytes from the Gentiles qualified for membership in Israel by baptism.
John the Baptist took this ceremony and adapted it as purification for the reign of the Messiah (Luke 3:3-6). By means of this rite, the people were consecrated to receive salvation; while Jesus, in submitting himself to John's ritual, was consecrated to bestow it (Matt. 3:13-15)." (Harper's Bible Dictionary, Madeleine S. Miller and J. Lane Miller, Harper & Brothers, Publishers, 1961, pg 60)

Infant Baptism
"The Bible is abundantly clear of what baptism is, who is it for, and what it accomplishes. In the Bible, only believers who had placed their faith in Christ were baptized - as a public testimony of their faith and identification with Him (Acts 2:38; Romans 6:3-4). Water baptism by immersion is a step of obedience after faith in Christ. It is a proclamation of faith in Christ, a statement of submission to Him, and an identification with His death, and resurrection.
With this in view, infant baptism is not a Biblical practice. An infant cannot place his or her faith in Christ. An infant cannot make a conscious decision to obey Christ. An infant cannot understand what water baptism symbolizes. The Bible does not record any infants being baptized." (www.gotquestions.org/infant-baptism.html)

Youth Baptism
"As a child matures in his faith and it is evident that he is truly born again, the father and/or mother should be perceptive as to when he is ready to receive such teaching. The spiritual maturity level of one child differs from that of another even in the same family.
Although this is an Old Testament story, the truth is still applicable. In Nehemiah 8:1-8, we read the account of Ezra, the scribe, reading the law to the people of Israel. He read it to the men and women and all who were able to understand. From 10:28 we learn that these included their sons and daughters. See also 8:8 for the same meaning. And so it must be today. It is most important that our children understand spiritual truths, and only wise Christian parents can discern when that time comes.
In many churches, when the parents of a child make it known to the pastor that he/she is wanting to be baptized, the pastor speaks with the child to decide if he/she is ready. This is a good and wise practice. It is vitally important that a child understands that neither baptism or communion saves him/her, but rather they are steps of obedience and remembrance of what Jesus did for us in providing for our salvation (Luke 22:19). (www.gotquestions.org/children-baptism-communion.html)

It is important to understand that the age of accountability is different for everyone. A child at the age of eight might not be able to understand spiritual truths just as infants are unable to understand them as well. An age requirement in order to be baptized is wrong. Every person is different in their spiritual maturity.
The museum, that is spoken of in a comment just made, has reconstructed a Christian church from the Byzantine-era. The information about the way the culture baptized at this particular era and church is not clear. However, if the Mormon church has particulars and specific facts with documentation, I'm sure everyone interested would like to see proof the LDS church has concerning youth baptisms.

"Doesn't Acts 2:38 teach that we must be baptized in order to be saved?
No. In the original Greek, Peter used the word "for" just like we use it in our everyday conversation. A child is punished for disobedience; not in order to be disobedient, but because he has been disobedient. A man arrested for stealing; not in order to steal; but because he has stolen. The same thing is true in baptism. We are baptized for the remission of sins; not to get our sins washed away, but to show that they have been washed away. A correct rendering of this passage is, "Repent all of you, and each one be baptized to declare the remission of your sins." (Answers to your Bible Questions, Charles Halff, The Christian Jew Foundation, 1972, pg 23) (italics added)