Water baptism is nothing apart from the individual's faith and own choice to be baptized - Heb 11:6 "But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him."
Infants are not capable of having faith, come to God or diligently seek God
Acts 2:38; Lk 13:3.5 before one can be baptized he must repent. Repentance is something the individual must choose to do, not a choice that can be made for the individual. Also, infants have no sins to repent of, have not transgressed the law of God (1 Jn 3:4)
Before one can be baptized he must confess "For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation." Rom 10:10 Again, not something infants are capable of doing.
In Mk 16:16 Jesus made belief a prerequisite before one can be baptized. Faith is not something one is innately born with but faith comes by hearing (Rom 10:17) and hearing there requires not only understanding in what is heard but an obedient hearing/listening, neither of which infants can do. Jn 6:45 those that 'cometh to Christ' are those that have been taught, heard and learned, none of which infants can do. The purpose God gave baptism is for the remission of sins, and again, infants have no sins to have remitted.
Those that have been baptized and become a Christian then have the responsibility to do good works (Eph 2:10; Mt 25:34-36); to carry out the great commission (Mt 28:19,29; Mk 16:15;16); to worship by singing, praying, giving as one has prospered, teaching, partaking of the Lord's Supper; (1 Cor 11:26-29) to encourage and exhort (Heb 10:22-15); edification (Rom 14:19),exhort and convince the gainsayer by doctrine, (Titus 1:9)......none of which can be done by an infant that has been baptized.
It would also seem if an infant were capable of choosing and being capable to believe he is also capable of choosing NOT to believe. How does one tell the believing infants from the no-believing ones?
(Side note: In Matt 18:6 Jesus uses an affectionate term of "little ones" in describing His disciples that have a purity and innocence as children. Note back in Matt 10 where Jesus gives what some refer to as the "limited commission" to His 12 disciples and refers to them as His "little ones" verse 42)