Iyov says the following (6:9)
וְיֹאֵ֣ל אֱ֭לוֹהַּ וִֽידַכְּאֵ֑נִי יַתֵּ֥ר יָ֝ד֗וֹ וִֽיבַצְּעֵֽנִי׃, Even that it would please God to crush me; that He would let loose His hand, and cut me off!
Rashi explains that he wanted to die.
Instead of beseeching Hashem to end his life, why didn’t Iyov himself just commit suicide?
Iyov believes in God, and believes that God is intentionally causing him to suffer, but he cannot figure out why. He is struggling to make sense of his suffering in terms of his relationship with and belief in God.
If he would commit suicide, he would be abdicating on that moral challenge, and "cheating" God, as it were.
When he tries to understand why God did not go all the way and kill him, and he expresses his wish that God would have done that, that opens new ways of thinking for him, allowing him to come to understand what God want from him, and why God pushed him almost to death and passed the point where he wished for death, but still kept him alive.
The Talmud [[Bava Kamma 91b]] says that you may not injure yourself, a fortiori commit suicide.
