Remember the superlatives and use of hyperbole by the Eastern poetry, expressing the feelings of the heart in strong imagery. Jeremiah suffered many persecutions, and rejection by the people he was calling to return to God.
In chap. 20, he had just been beaten and put in the stocks (vs. 2), mocked by those he warned (vs. 7), reproached and derided for doing God's will (vs. 8) rejected by his friends (vs. 10).
This was just one among many times that Jeremiah suffered persecution for trying to warn the people of the judgment that was about to come upon them in the Babylonian captivity. No one wanted to hear it. Their constant response was to ridicule and spit upon Jeremiah. They didn't want him to show them their sins, or to disrupt their comfort.
Jeremiah's cry to God that he wished he had never been born was during deepest despair and in an Eastern style of hyperbole. Just as in Jer. 4:19,
"My bowels, my bowels! I am pained [at] the walls of my heart, Make a noise for me doth My heart, I am not silent, For the voice of a trumpet I have heard, O my soul -- a shout of battle!" (YLT)
Or as in Jer. 9:1,
"Who doth make my head waters, And mine eye a fountain of tears? And I weep by day and by night, For the wounded of the daughter of my people." (YLT)
Or as in Jer. 10:19,
"Wo to me for my breaking, Grievious hath been my smiting, And I said, Only, this [is] my sickness, and I bear it." (YLT)
And, again as in Jer. 15:10,
"Woe is me, my mother, That you have borne me, A man of strife and a man of contention to the whole earth! ..." (NKJV)
It was an exclamation of hyperbole in the Eastern manner, a cry from the heart caused by much suffering, and frustration. His calling to the people was a burning fire within him (20:9) that he could not ignore. But, it caused him persecution and suffering all of his life.