This is actually very faulty logic on at least two fronts. First, it presumes that God is loving. If God is evil, and there are some cultures that have actually presented God as being evil, then the universal existence of evil would be proof that God does exist. In actuality, the existence of evil doesn't prove that God doesn't exist, it simply calls into question His nature. Using the existence of evil as proof that God doesn't exist is like pointing at a pile of bear poop and claiming it proves that there are no bears. Is the bear poop unpleasant? Definitely. However, its very existence is a clear sign that there is a very large and possibly unfriendly something nearby.
The second flaw in the logic of arguing against God's existence by pointing to the existence of evil is that it presumes that there could be no possible reason for a loving God to allow it to persist. It presumes that evil serves no good purpose. Bear poop is unpleasant, but it does serve a good purpose. Not only does it serve as a warning sign that bears are nearby, but it also fertilizes the ground and creates growth.
Rather than attempting to argue that the bear doesn't exist when coming across bear poop, the wise person stops to study the poop and try to understand its meaning. The tracker knows that if the poop is hot, the bear's not very far away at all and it's either time to prepare a strong defense or else change directions. An experienced woodsman might even be able to tell how hungry the bear is based on how large the pile of poop is, which means being able to determine how aggressive the bear is likely to be.
Evil, like bear poop, is proof of an unseen reality. You can either ignore that reality and perish, or pay attention and learn something. The choice is up to you.