It is difficult to judge the motives of Theodore, but his reluctance to say that the Apostle Thomas confessed the divinity of Christ probably stems from his Christology.
Theodore was a sustainer of the Logos-anthropos or Antiochene Christological school, which tried to understand the Incarnation as the union of the Word with a man (Greek: ánthropos). The Antiochene school used this model in order to emphasize the completeness of what (we would call) Jesus’ human nature.
A possible pitfall, however, is emphasizing the completeness of the human nature so much as to affirm that Jesus is (in addition to a Divine Person or Hypostasis) a human person: that is the error of Nestorius.
It is debatable whether Theodore actually intended to teach this error;* nevertheless, that is certainly how the Second Council of Constantinople interpreted his commentary on John 20:28:
If anyone defends the impious Theodore of Mopsuestia, who has said that the Word of God is one person, but that another person is Christ … [and] likewise has said that the profession of faith made by Thomas when he had, after the resurrection, touched the hands and the side of the Lord, viz.: My Lord and my God, was not said in reference to Christ, but that Thomas, filled with wonder at the miracle of the resurrection, thus thanked God who had raised up Christ …: let him be anathema (Acts of the Second Council of Constantinople, Can. 12, Denzinger-Hünermann 434).
The Council here is interpreting Theodore as espousing a Nestorian-like distinction between the Person of the Word and Jesus’ (supposed) human person. If this is the case, Theodore is effectively arguing that the Apostle Thomas cannot call the human Jesus “God,” because the human Jesus is merely a human person (not a Divine Person, as orthodox Christology holds).
* The Antiochene, or Logos-anthropos, model is not necessarily heretical. We still see echoes of it in the Te Deum (a hymn dating from the fourth century, before the Council of Ephesus):
Tu ad liberandum suscepturus hominem, non horruisti Virginis uterum.
In order to free [man], you took on man; you did not spurn the Virgin’s womb.
Here, however, when we say that God “took on man”, we take “man” to mean what we would call “human nature” today.