There are two views of why the scribes said to themselves that Jesus is blaspheming:
They see the implication of Jesus’ statement that the paralytic’s sins are forgiven: that he thus presents himself as God, who alone can absolve guilt. If one assumes that Jesus is only a man, then his statement would be blasphemous. The fact that he has full rights to forgive sins, because he is God himself, is something these scribes refuse to acknowledge, but they dare not make their accusation of blasphemy public, since he has by now shown his divine power through his miracles.
The scribes accuse Jesus of blasphemy because he proclaimed the forgiveness of sins, something that God alone can do (Mark 2:7; Luke 5:21; see also Exodus 34:6–10; Isaiah 43:25–28, Isaiah 44:22). Jewish tradition would not even allow the Messiah to do this. However, God could, of course, always proclaim forgiveness through a prophet (see 2 Samuel 12:13). There are thus two possibilities: that either Jesus claimed for himself a prerogative that properly only belongs to God, or he spoke from his prophetic office. Since Matthew 9:4 clearly shows how this prophetic gift was present with Jesus, and since he uses the passive form when proclaiming the forgiveness in both Matthew 9:2 and Matthew 9:5, we should affirm the second possibility here. The problem here was that the scribes taught that the gift of prophecy had already ceased at the time, so this is why they accused Jesus of blasphemy. Of course, the punishment for blasphemy is death by stoning (see Leviticus 24:14; 1 Kings 21:10,1 Kings 21:13).
Interpretation 1:
The scribes immediately recognize the implications of Jesus’ proclamation that the paralytic’s sins are forgiven. After all, by doing this Jesus presents himself as God, who alone is able to absolve guilt. If one were to work with the assumption that he is only a man from Nazareth and a normal citizen of Capernaum, then what he does here would be interpreted as blasphemous. In Israel, blasphemy was punishable by death. The thoughts of the scribes here betray their enmity towards him.1
The scribes know full well that the forgiveness of sins is the exclusive domain of God as the One against whom man has sinned. As such they regard this statement by Jesus as blasphemous, given that he attributes divine power to himself. The fact that he has full rights to do so, because he is God himself, is something these scribes are unwilling to acknowledge. This accusation of blasphemy is something they, at least for the time being, keep to themselves, however, as they dare not publicly accuse Jesus, who had by now revealed his divine power through his miracles.2
Interpretation 2:
The scribes accuse Jesus of blasphemy because he proclaimed the forgiveness of sins, something that God alone can do (Mark 2:7; Luke 5:21; see also Exodus 34:6–10; Isaiah 43:25–28, Isaiah 44:22). In Jewish tradition this privilege would not even be accorded the Messiah himself. Nonetheless, God could, of course, always act through a prophet as his vessel (see 2 Samuel 12:13). There are therefore two possibilities: that either Jesus claimed for himself a prerogative that properly only belongs to God, or he spoke from his prophetic office. In light of the fact that Matthew 9:4 clearly shows how this prophetic gift was present with Jesus and in light of the passive form employed by Jesus when proclaiming the forgiveness in both Matthew 9:2 and Matthew 9:5, we should affirm the second possibility here. The problem here was that the scribes had taught that the gift of prophecy had already ceased at the time, and it is this that formed the basis of their accusation of blasphemy. Of course, the punishment for blasphemy is death by stoning (see Leviticus 24:14; 1 Kings 21:10, 1 Kings 21:13).3
3 Alors, quelques scribes dirent au-dedans d'eux: Cet homme blasphème.