Why does the Muslim not believe in reincarnation?

Everything in the universe falls under the control of the Creator. He alone possesses comprehensive and absolute knowledge, and the ability and strength to subjugate everything to His will. The sun, the planets, the galaxies all function thoroughly since the beginning of the creation, and these same thoroughness and ability apply to the creation of mankind. The harmony between the human bodies and their souls proves that it is impossible to make such souls inhabit animals' bodies or roam among the plants and insects, and reincarnation is even impossible among human beings. Allah Almighty has distinguished man with the mind and knowledge and has made him a vicegerent on earth. He preferred him and honored him and granted him a higher status than many of His creatures. And out of the Creator's wisdom and justice, there will be the Day of Judgment when Allah alone shall resurrect the creatures and bring them to account. They will end up either in Paradise or in Hellfire, and all the good and evil deeds will be weighed on that Day.

{So whoever does an atom’s weight of good will see it, and whoever does an atom’s weight of evil will see it.} [86] Surat az-Zalzalah: 7-8.

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