Why does he say "Ba'ar [Anochi me'Ish]"?
Sanhedrin 70b: "Divrei l'Mu'el... Asher Yisarto Imo" - Bas Sheva tied Shlomo to a beam and lashed him (for eating too much). Shlomo admitted to his mother - "Ki Ba'ar Anochi..." - I am more foolish than Noach - "va'Yachel Noach Ish ha'Adamah."
Rashi: I relied on my Chachmah, in a matter in which Hashem worried lest one come to sin.
Malbim: Shlomo answered what the Chachamim asked about creation of the world and secrets of Ma'ase Bereishis. Based on his Teshuvah, these Chachamim investigated in the way of philosophy, and wanted to expound what is above and what is below, what is in front of and what is in back. They said ideas based on their Sechel, like philosophers of the generation investigated, and they concluded Cheres (worthless ideas). Agur answered, how can they seek from him these exalted matters that are not known via human investigation, only via Divine revelation to Kadosh people. It is called Da'as Kedoshim. How can I (Agur) know this? I am Ba'ar 1 !
Malbim: He lowered himself further - I lack even simple Da'as that all people have - what is sensed, or axioms planted in everyone's Sechel. One who lacks this is called Ba'ar, which is like Behemah - animalistic, and not human.
Why did he say that he has no Binas Adam?
Sanhedrin 70b: When Bas Sheva chastised Shlomo, he said 'I lack the Binah of Adam ha'Rishon.'
Malbim: The order of knowledge is Chachmah, Binah and Da'as. Chachmah is first; it is not known via proofs of Da'as. Only Hashem informed the laws of Chachmah in His Torah and taught people. After Chachmah is Binah. After receiving the laws of Chachmah from Elokim, a Ba'al Binah, who understands a matter amidst another matter, can contemplate their reasons and derive a matter from a matter. After Binah, he comes to Da'as - knowing something clearly, like one knows what is sensed, or axioms. One who reached this level, Ru'ach Elokim appears to him to inform him Da'as Kedoshim - truths if secrets of Elokim in Ma'ase Bereishis and Ma'ase Merkavah, of the creation and conduct, connections of the worlds
Malbim: He lowered himself further - I lack even simple Binah that many people have.