Why does Justin Martyr say that those who are unworthy of seeing God will become imprisoned in animal bodies? In Dialogue with Trypho, an early Christian text, Justin Martyr and a Jew named Trypho discuss the nature of the soul and its interaction with God. After talking a bit about if animals could see God and if that was any different than humans, this conversation happens (translation taken from here):

[Trypho asked,] &quot;'What, then, is the advantage to those who have seen [God]? or what has he who has seen more than he who has not seen, unless he remember this fact, that he has seen?'
&quot;'I cannot tell,' I [Justin Martyr] answered.
&quot;'And what do those suffer who are judged to be unworthy of this spectacle?' said he.
&quot;'They are imprisoned in the bodies of certain wild beasts, and this is their punishment.'

This seems like a really bizarre conclusion to me, yet Trypho seems to take it in stride, moving on to his next argument. Why would Justin Martyr assert that those who see God and yet were unworthy would become imprisoned in the bodies of certain wild animals? Was this a commonly held belief in his lifetime (in the years A.D. 100–165)?
First, keep in mind that Trypho is (almost certainly) a fictional character. He takes the statement in stride because it suits Justin's purpose. 

To answer your question, transmigration of the soul  was a common belief in many Hellenistic philosophies. Note that Trypho stated at the beginning of the dialog that he studied under Corinthus the Socratic in Argos. It is not unreasonable that he would be familiar with if not accept the concept.

Now the question becomes ' Did Justin teach transmigration?' Read on. It seams to me that he is leading Trypho to reject the idea. The section closes with 


  Trypho: Therefore souls neither see God nor transmigrate into other bodies; for they would know that so they are punished, and they would be afraid to commit even the most trivial sin afterwards. But that they can perceive that God exists, and that righteousness and piety are honourable, I also quite agree with you.
  
  Justin: You are right.