Even though I reject religion, I do not agree with you on this one. The most common answer that theists often respond with is
free will. Of course this leaves the question:
does free will exist? I would argue that free will does exist, but that is not what I will be arguing.
Irenaeus stated that God made humans imperfect and is therefore partly responsible for the existence of evil. To make humans perfect would take away their freedom to live in accordance with God’s will. By creating imperfect humans, individuals are given the chance to develop and grow through a soul-making process into children of God. Irenaeus stated that eventually good will overcome evil and suffering.
Alvin Plantinga argued something similar, but I won’t go into specifics.
I feel like there are many theodicies concerning the evil in humans, but let’s assume that you want to know about earthquakes, tsunamis, predators, etc.
The problem with needing a theodicy for this, is that it is not moral evil. Is it immoral for a lightning bolt to strike a tree? Obviously not.
We might think that tsunamis are
bad but does that make them
evil?
The following question would be
Why doesn’t God stop them happening? My best answer is that we only see them as
bad because they go against what we
want. However, most religions already have rules that go against what humans want (sex before marriage, lying, temptation, etc.) so it’s not really a problem.
I am not a religious person, but I do not believe that the logical problem of evil is actually a good argument against theism.
Hope this helps! :)