Just to be clear, the pre-existence of souls discussed in the Second Council of Constantinople is a teaching specifically put forth by Origen of Alexandria which said a bit more than "human souls existed prior to their human bodies." The following teaching is what was condemned at the council.
In its fullness, the teaching stated that all intelligent souls were created before any of the physical world; furthermore, they were created in union with God. Some souls grew weary of loving God and became demons; some grew to love God moderately less and became humans; some remained in God and became angels.
In the First of the Anathemas of the Emperor Justinian Against Origen, he states:
Whoever says or thinks that human souls pre-existed, i.e., that they had previously been spirits and holy powers, but that, satiated with the vision of God, they had turned to evil, and in this way the divine love in them had died out ... let him be anathema.
Essentially, Origen's teaching states something that is not possible: for a soul to know and love God fully and to turn away. God's glory and goodness means that any soul/spirit that truly knows and loves God would never choose anything else. Hence, a soul cannot grow weary of God.
In addition to the source quoted above, the Anathemas Against Origen (in the same document) give some more things that were found particularly objectionable in Origen's teaching such as:
- Jesus' human soul was not always united with God the Word (contradicts teachings on the Trinity)
- The sun, moon, and stars have rational souls (they are just physical objects)
- At the end of the time, there will be no material world (contradicts the physical resurrection of the human body)
There are many other things in there to be read, but I will not cover all of them here. Generally, it seems in the document that they state the particular parts of teaching of the pre-existence of souls that are in conflict with doctrine without offering specific arguments against them. This leads me to believe that the arguments against Origen's teaching are simply the arguments in favor of the doctrines of the Church which would be located elsewhere.
Sources: Wikipedia: Origen, Second Council Constantinople.