Why is the Testament of Solomon not considered canon?

Why is the Testament of Solomon not considered canon?

Simply put, no one believes it was inspired by God. We do not even know if it was of Jewish or Christian origin or both.

The Testament of Solomon is extant in unedited Semitic manuscripts and in Greek.

This pseudepigraphon is neither so late nor so early as some older scholars claimed. Date for the original compilation which incorporates a first-century A.D. Jewish composition that the original Jewish work is to be identified with the Solomonic incantations cited by Josephus near the end of the first century A.D. Josephus does not appear to be referring to a particular text but to the numerous liquid traditions about Solomon's control over demons. McCown (pp. 38-43) argued that the original language is Greek, except for a possible Semitic original in recension A in the list of decani (18:24-40 [H]). He suggested that the provenance, in ascending order of probability, is Galilean, Egyptian, or Asian; the section containing the list of decani, however, is Egyptian (p. 42). Frey (col. 456) proposed an Egyptian provenance for the entire work.

The pseudepigraphon is either a Jewish composition which was eventually reworked by a Christian or a Christian writing which incorporated some Jewish material. Clearly Christian passages are found in sections. These passages emphasize the cross and virgin birth.

The Testament of Solomon contains 130 sections, according to Conybeare's translation (26 chapters according to McCown's edition of the longest recension). The work is called a testament because Solomon writes the diatheken (130=26:8) in order that those who read it may pray and heed the last things (tois eschatois). This exhortation mirrors Solomon's egregious error, his lust for a Shunammite girl and subsequent idolatry. Earlier (66=15:13) Solomon states that he wrote his testament before his death so that the children of Israel would know the powers and shapes of the demons, and the names of the angels who have power over them.

The pseudepigraphon recounts how Solomon is able to build the Temple by defeating demons and employing their skills by means of a ring and its seal given to him by the Archangel Michael. Solomon's greatness is acknowledged by a visit from the Queen of the South, who is a witch, and by a letter from the king of the Arabs. Solomon succeeds in building the Temple only to fall into idolatry through lust for a Shunammite girl.

If the Testament of Solomon is not late, as early scholars claimed, then it belongs in the Pseudepigrapha. In light of the emphasis upon demons and angels and the central concern for the Temple it will be interesting to see if there is a relation between this pseudepigraphon and the Qumranic Temple Scroll. - Testament of Solomon

Wikipedia has the following to say about its dating and authorship:

Scholarly opinion on when the testament was written varies widely. Despite the text's claim to have been a first-hand account of King Solomon's construction of the Temple of Jerusalem, suggested dates for its composition range between the end of the 1st century CE and the high medieval period. Also disputed is whether it had a Christian or Jewish origin. Mid-twentieth century scholarship tended to agree that much of its content "reflects the first-century Judaism in Palestine" and includes material much earlier than its composition. However, scholars both before (e.g., Istrin) and after (e.g., Schwarz) proposed other solutions based upon the varied manuscript evidence. Because of the text's various forms, produced over centuries by distinct scribes, the author or authors of the text remain unknown. The text was originally written in Greek and contains numerous theological and magical themes ranging from Christianity and Judaism to Greek mythology and astrology that possibly hint at a Christian writer with a Greek background.

The Testament of Solomon may be read in its entirety here.