Perhaps is was the just the very natural wearing down of a man struck with a constant stream of afflictions. Bear in mind that there were multiple afflictions (50 independent calamaties according to Shemos Rabbah 23:9) which spanned the space of a year (Mishna Eduyos 2:10).
Whilst not a direct answer perhaps we can draw a tentative conclusion perhaps based on the Avos D'Rabbi Nosson 37:13
There it writes about his friends' interaction with him:
ואינו נבהל להשיב זה אליהו בן ברכאל הבוזי שנא׳ (איוב ל״ב:ז׳) אמרתי ימים ידברו מלמד שהיו יושבין ושותקין לפני איוב עמד היו עומדין ישב היו יושבין אכל היו אוכלין שתה היו שותין עד שנטל מהם רשות שנא׳ (שם ג) אחרי כן פתח איוב את פיהו ויקלל את יומו ואמר יאבד יום אולד בו והלילה אמר הורה גבר. יאבד יום שבא אבי אצל אמי ואמרה לו אני הרה. ומניין שלא ענו בערבוביא שנאמר ויען איוב ויאמר. ויען אליפז התימני ויאמר. ויען בלדד השוחי ויאמר. ויען צופר הנעמתי ויאמר. ויען אליהוא בן ברכאל הבוזי ויאמר סדרן הכתוב אחד אחד (אלא) להודיע לכל באי עולם שאין חכם מדבר לפני מי שגדול הימנו בחכמה. ואינו נכנם לתוך דברי חבירו. ואינו נבהל להשיב. שואל כענין זה יהודה שנא׳ (בראשית מ״ג:ט׳) אנכי אערבנו. שואל שלא כענין זה ראובן שנא׳ (שם מב) ויאמר ראובן אל אביו את שני בני תמית. ואומר על ראשון ראשון זה יעקב וי״א זו שרה ועל אחרון אחרון אלו אנשי חרן . ומודה על האמת זה משה שנא׳ (דברים ה׳:כ״ה) ויאמר ה׳ אלי [וגו׳] הטיבו (את) [כל] אשר דברו. וכן הקב״ה הודה על האמת שנא׳ (במדבר כ״ז:ז׳) כן בנות צלפחד דוברות:
And he does not become agitated and respond too quickly.
This is Elihu ben Berakhel HaBuzi, as it says (Job 32:7), “I said to myself: Let age speak first.” This teaches that they were sitting in silence before Job. When he would stand up, they would stand up. When he would sit down again, they would sit down again. When he ate, they would eat. When he drank, they would drink. Finally, he asked permission to speak, as it says (Job 3:1, 3), “Afterward, Job began to speak, and cursed the day of his birth.” And he said, “Perish the day on which I was born, and the night it was announced: A male has been conceived!” Perish the day that my father came to my mother and she told him: I am pregnant. And how do we know that they did not all start speaking at the same time? For it says (Job 3:2), “Job answered and said…” and then (Job 4:1), “Elifaz HaTeimani answered and said…” and then (Job 8:1), “Bildad HaShukhi answered and said…” and then (Job 11:1), “Tzofar HaNa’amati answered and said…” and then (Job. 32:6), “Elihu ben Berakhel HaBuzi answered and said….” The book lays them out one at a time (however), to let everyone know that a wise person does not speak before someone who is greater in wisdom. And does not interrupt his fellow. And does not become agitated and respond quickly. He asks appropriately. This is Judah, as it says (Genesis 43:9), “I will pledge myself for him.” He asks inappropriately. This is Reuben, as its says (Genesis 42:3), “Reuben said to his father: Let my two sons die!” He speaks of first things first. This is Jacob. And some say this is Sarah. And last things last. These are the men of Haran. And he admits to what is true. This is Moses, as it says (Deuteronomy 5:25), “The Eternal said to me…they did well to speak thus.” So, too, did the Holy Blessed One admit to what was true, as it says (Numbers 27:7), “The daughters of Tzelophechad have spoken correctly.” (Sefaria translation)
So perhaps from purely a human psychological level, whilst it would have been comforting to have friends there with him as he was suffering, it may have been equally frustrating as they didn't do much else until they were granted the opening to speak. Obviously we are dealing with a great tzaddik and therefore it is not our place to suggest chas veshalom that he lacked control, and indeed his righteousness is listed in numerous places (e.g. Avos D'Rabbi Nosson 2:5 and Devarim Rabbah 2:4 to name a couple) - but ultimately he was still human, and perhaps at least on our level, we can suggest that this may have been the proverbial 'straw that broke the camel's back'.
