I believe that His wrath only exists from our perspective. Those who rejected him experience his love as a burning fire and that is called metaphorically "His wrath". God doesn't literally suffer from passions or have changing emotions though. He is love immutable and unchangeable.
A book I was reading about St Ephrem really opened my eyes on how to understand certain things said about God in the Bible:
"What God has allowed to be said of himself in the Bible is, for Ephrem, a primary source for any human knowledge of God. The 'names' of God and the various types and symbols in Scripture constitute meeting points between God and humanity: God in his divine condescension has lowered Himself to the level of human understanding.
From the human side, if advantage is to be taken of this opportunity, offered by God, of a way towards knowledge of Himself, two things are essential,... in the first place we must not make the ungrateful mistake of taking the names and metaphors used by God in Scripture literaly...
Ephrem in his role as theologian, is naturally primarily interesting in penetrating to the interior meaning of Scripture, a realm explored by the eye of discernment (purshana) and this inner eye of faith.
Indeed he stresses that to stop at Scriptures outward statements about God and to take them literally is both dangerous- in that it will lead to misconceptions about Gods nature- and at the same time a sign of utter ingratitude for, and misunderstanding of Gods condescension in allowing himself to be spoken of in human language at all.
Saint Ephrem the Syrian states:
If someone concentrates his attention
solely on the metaphors used of God's majesty,
he abuses and misrepresents that majesty
by means of those metaphors
with which God has clothed Himself for humanities
own benefit,
and he is ungrateful to that Grace
which has bent down its stature to the level of human
childishness;
even though God has nothing in common with it.
He clothed Himself in the likeness of humanity
in order to bring humanity to the likeness of Himself.
-St Ephrem : Paradise 11:6