Infant Communion

While doing kitchen work today, I was listening to Issues Etc on the topic of infant communion.  The guest said some good stuff.  But one big thing confused me.

Much of his argument [against infant communion] was based on the fact that Jesus instituted baptism in a different way than He instituted the Lord's Supper.  He said that one was directed to the recipients and one was directed to the ministers.  He said that Jesus did not institute baptism by baptizing people, but by telling the ministers what to do, what to say, and why.  He said that Jesus instituted the Lord's Supper by speaking directly to the recipients (through their mental faculties).

But ...

Jesus was baptizing people.  Jesus and His apostles baptized more than John and his disciples (John 3 and 4:1-2). 

First, Jesus baptized.  And He catechized on baptism (to Nicodemus, for example).  Then later, Matthew shows us the specifics of how He told His apostles to administer baptism.  On Maundy Thursday, Jesus communed His disciples.  Then later, we see what Paul wrote about specific instructions regarding how to administer the Lord's Supper that Jesus had instituted earlier. 

Why are those different from each other?