Good question, and welcome to BHB.
As you will find out very quickly if you continue to participate in BHB, perhaps the most important principle of hermeneutics is context. A good mantra for a site such as ours should be:
"A text without a context is a pretext."
The habit of contextualizing a text saves us students of the Bible from jumping to conclusions when faced with apparent contradictions in Scripture. You did well in comparing one verse in Job to another verse in the same book. To get rid of the apparent contradiction between Job 2:10 and 3:1, however, we need to consider the verses in the context of the whole of Job and even the whole of Scripture.
Let's set the stage for an answer to your question by looking at Job 1:20-22, which is preceded by Job's having experienced three tragedies back to back, including the loss of all his children:
"Then Job arose and tore his robe and shaved his head, and he fell to the ground and worshiped. He said, 'Naked I came from my mother's womb, And naked I shall return there. The LORD gave and the LORD has taken away. Blessed be the name of the LORD.' Through all this Job did not sin nor did he blame God" (1:20-22).
In his behavior Job was not prey to what I call "easy believism." He recognized clearly that God, despite the tragedies Job had just experienced, was still Sovereign and in control of Job's life. It is easy to believe in a god (small G) who gives us only what we want and not what we don't want. It is not so easy to believe in the one true God who in His infinite wisdom gives us both! Job was not an easy believer!
The words "Curse God and die" came from the mouth of Job's supportive(!) wife. What triggered the words was Job's having been stricken by Satan--with God's permission--with painful and hideous "boils from the sole of his foot to the crown of his head" (2:7). What was Job's response to this near blasphemy coming from his wife? Job said,
"'You speak as one of the foolish women speaks. Shall we indeed accept good from God and not accept adversity?' In all this Job did not sin with his lips."
Are we justified at this point in concluding that given his "druthers" Job would still have chosen disaster over blessing? No. Job was not a masochist saying to God, "Pile it on, Lord, it hurts so good." He was, rather, a realist who bowed to the sovereign will of the God he worshiped (again, see 1:20).
When we come to chapter 3 (entitled in the NASB "Job's Lament") after his three friends had joined him in silence for an entire week, we read
". . . Job opened his mouth and cursed the day of his birth. And Job said, 'Let the day perish on which I was to be born, And the night which said, A boy is conceived. May that day be darkness; Let not God above care for it, Nor light shine on it'" (vv.1-4).
Is wishing you had never been born tantamount to cursing God? Before you answer, consider the words of another saint of God who endured suffering beyond human comprehension and subsequently cried out
"My God, my God, why have You forsaken me? Far from my deliverance are the words of my groaning. O my God, I cry by day, but You do not answer; And by night, but I have no rest. Yet You are holy, O You who are enthroned upon the praises of Israel. In You our fathers trusted; They trusted and You delivered them. . . . But I am a worm and not a man, A reproach of men and despised by the people" (Psalm 22:1-4,6).
This prophetic psalm, which gives us remarkable details concerning the cross-death of Jesus Christ, underscores the role of emotions in giving voice to words that reflect accurately the inner turmoil of a saint. This saint, as with Job, felt he was being punished unfairly and unjustly but who knew in his heart he was actually called upon to endure for a greater good the seemingly inexplicable actions of a sovereign God.
Was Jesus truly forsaken of God while on the cross? No. If He were, why would His last words be,
"'Father, into your hands I commit my spirit.' Having said this, He breathed His last" (Luke 23:46).
No, Jesus was not forsaken of the Father, nor did the Father avert His eyes from His Son while Jesus as the Lamb of God was bearing away the sin of the world. Where some Christians have gotten the notion that God the Father turned His back on Jesus as He hung on the cross, I do not know. It is certainly not from Scripture.
Did Jesus feel forsaken by His God? Yes. Was He in fact forsaken? No.
Finally, did Job, like Jesus, feel forsaken by the God whom he worshiped? Perhaps yes. If you were to ask Job, "Job, were you in effect cursing God when you cursed the day you were born?", I suggest Job would have answered invariably, "No! God forbid. But I certainly felt as if I were accursed, knowing as I did that I was blameless before God!"
Job knew in his heart that God had adjudged him as blameless in His sight. God Himself had said,
"'For there is no one like [Job] on earth, a blameless and upright man, fearing God and turning away from evil'" (1:8).
Despite his moments of despair, perplexity, and incomplete knowledge about the inscrutable ways of the transcendent God whom he worshiped, Job did not sin with his lips. Had he done so, the book of Job may not have become part of sacred Scripture!