Elihu will state his view because he really does care, pastorally. The others are anxious to win an argument, have the last word.
It is possible of course for a man to be self-deceived about this matter and to imagine that zeal for his own glory is zeal for God. He feels compelled to speak, not because he loves the truth, but because he loves the sound of his own words and the expression of his own wisdom. Can a believer escape this self-deception and know that he is speaking out of a genuine zeal for God? Yes, but not without the constant habitual practicing of humility before God which struggles to put to death every rearing of pride’s head. In this process of sanctification, often a person will deny themselves the opportunity to speak because they are not sure that pride is not mixed in with their speaking. But though not entirely without sin, but with a clear and deep love for the truth, they learn to defend the glory of God with a true heart that loves truth more than self. Elihu had reached this point and now he felt compelled to speak and it was his duty to do so.
The act of speaking would bring him relief. God had put within him strong desires, and those desires must find expression. It is a good thing when we are filled with the Spirit of God and he is prompting us to speak so that we cannot remain silent. God gives man the capacity to communicate through words and gives a strong sense of satisfaction in communicating truth. The same urgency to speak is found in others in Scripture. Christ was compelled to speak and quotes Psalm 69:9, ‘The zeal of thine house hath eaten me up’ (John 2:17). Peter and John had to speak though it brought persecution on them, ‘For we cannot but speak the things which we have seen and heard’ (Acts 4:20). Even Baalam the false prophet had to speak, ‘Must I not take heed to speak that which the LORD hath put in my mouth?’ (Numbers 23:12). Elihu felt like a wineskin with fermenting new wine in it causing pressure to build up on the inside. This pressure comes from a realisation of the value of the words that need to be spoken.