Rather, ask “Why did Jesus leave out the Psalms ?
Hint: He did not leave out the Psalms (or Daniel). He included them in what has come down to us in the Gospels although he did not use the triplet phrase “Torah, Neviim, v’Ketuvim” as is done today, but rather just “Torah v’Neviim”
I have to disagree with you. (from the article)
Christ Declares The Hebrew Canon The Word of God.
Luke 24:44 And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.
Luke 24:45 Then opened he their understanding, that they might understand the scriptures,
Here in the above verse, Jesus divides the written word of God into three categories. The Hebrew Bible, known by the acronym TaNaKh, has these three divisions, first the Torah, the first five books of Moses, second the Nevi’im or Prophets, and third the Ketuvim or Writings. Christ was appearing to the disciples shortly after His resurrection and He was expounding to His disciples on the testimony of the scriptures about Himself, from one end of the Bible to the other. From the beginning at Moses; next to the prophets; and then on to the last division that began with Psalms; Christ explained from the Hebrew Bible, the TaNaKh, how it revealed Him to be the Messiah.