The difference ultimately stems from different views of the state of Fallen Man and the purpose of baptism itself.
Catholics believe that Mankind in it’s Fallen state is completely corrupted and unable to move towards salvation without being first called by the Grace of God. This Grace calls us and enables us to respond freely to the offer of salvation, but only if God first calls us. In calling us, God wipes away the stain of Original Sin, which is what otherwise deprives us of the chance to hear His call.
Catholics believe this literal wiping away of Original Sin and Call to Grace comes at the sacrament of Baptism. In Protestant circles, this belief is known as “Baptismal regeneration.” Importantly, Catholics (and those Protestants who also believe in baptismal regeneration, particularly the Lutherans) believe that the work and power of Baptism is 100% God’s, with nothing being done by the person being baptized. That means whether the person is a “believer” or not does not matter, and in fact saying so would limit the power of God!
Your generic evangelical, however believes that salvation comes merely from making “the Decision for Christ” and that baptism is purely symbolic of this commitment. Since they follow this “decisional regeneration” model, baptizing infants of course is meaningless. This of course implies that God needs the person’s permission to call them to grace, which smacks of “works-based salvation” that they all declare invalid.
Your friend might try to say that in saying this you’re arguing for a Predestination style belief. This is NOT true. Predestination believing Protestants think that man has no free will at all, can neither choose nor reject salvation, and is saved (or damned) because God chose them for that destiny from before the beginning of the universe. Catholics and Evangelical Christians (for the most part) both reject this.
Rather, we simply believe that while we are free to accept or reject God’s grace, it’s up to God alone to cleanse us of original sin and call us to Him. And we believe he does this in Baptism. (Compare the parable in Matthew 22:1-14; Some guests declined or didn’t properly prepare themselves, but NO ONE could come unless they were invited)
Note too, that we believe Baptism can take several forms, the most common of which is with water. But the Church teaches that Baptism (and God) cannot be limited if there is no one to perform the act, or if there is no means available. (Take a look at Church teachings on “Baptism of Desire” or “Baptism of Blood”). So if your friend doesn’t like the implication that God need’s a person on hand to administer Baptism, remind him that he doesn’t but simply chooses to use us Christians on earth as his ministers because of His “overabundance of Grace”, in which we are all called to share in Christ’s ministry.
It might be useful to show your friend that infant baptism is not just “a Catholic thing”, which in his mind is probably equated with “unbiblical/wrong”. Here’s a defense of infant baptism written from a Lutheran Protestant perspective: