Wrath" of God is the consequence of the Supreme Law of God - the just punishment of man for rejecting, for violating the Will of God, for not obeying His Commandments.
"Wrath" of God is also the consequence of man's failure to perceive the warnings of the voice of his conscience, of his reason, the consequence of his rejection of the Will of God proclaimed by the Righteous.
"Wrath" of God is manifested by the operation of His beneficent Laws, which are always governed by the all-encompassing Love of God the Father for His Creation - man.
Man's anger is a feeling of vehement protest, indignation, strong indignation at something.
It is a negative quality of man's character, one of the manifestations of his violation of the Commandments of God, the Teachings of Jesus Christ.