Man has free will. He can choose to do good or bad.
Does God have free will? Can God choose to do bad things?
If we say that god does only good, isn't that putting a limitation on him?
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G-d can do bad, but does not. As Ramchal explains in Derech Hashem, G-d is the ultimate source of good, and created the world to bestow goodness on others. Doing bad would be against G-d's purpose. G-d gave humans the choice between good and bad so that they can exercise free will and so-to-speak "earn" their reward.
In other words, the opportunity to do bad is ultimately for their good, because it makes their choice to do good much more meaningful. So in a way, even the "bad" of creation was created with a good purpose.
Obviously, these topics are super deep. This is the original source for my comments, to the best of my understanding and with an attempt to make it as accessible as possible.
Of course. God says through the prophet Isaiah:
‘Oseh shalom uvoreh ra’ [I make peace and create evil]; Ani HaShem ‘oseh chol elleh [I am the Lord who does all these things] [Isaiah 45:5,7]
Our faith consists of believing that whatever God does that may appear "evil" to us ultimately has a "good" purpose.
I once heard a rabbi (whose name I will not mention for privacy reasons) say an interesting interpretation of the episode of the golden calf (Exodus 32). During this episode, G-d makes what according to him an "evil" decree to destroy all of Israel. However, Moses pleaded with G-d, and like Abraham, questioned the divine decree. Thus, God repented of His "evil" (Exodus 32, 14). Now, I do not agree with this interpretation at all. But it does seem to suggest that G-d can do evil. In other words, G-d has free will, which begs the question, is G-d's "will" similar to human will?
“Humans are given free will. If a person wants to take the good path and be righteous, he is free to do so; and if he desires to take the evil one and be wicked, he can do so ... The Creator doesn’t preordain man to be good or evil” (Mishneh Torah, Teshuvah 5:1–23).
Thus, people have a yetzer ha’ra, an evil inclination, and a yetzer ha’tov, a good inclination (BT, Berakhot 61a). People can choose to be good or evil. This begs the question, why does G-d "allow" humans to act evil? Rabbi Harold Kushner opines that G-d lacks the power to prevent evil. He seems to say that G-d is not all-powerful. Others insist that G-d can prevent evil, but choose not to; so humans can exercise their free will. Maimonides felt that G-d is good and does not do evil. I agree with Maimonides.
Since G-d is transcendent, it follows that He is not subjected to the laws of nature (ie no limitations). Since humans have free will, so does G-d, but G-d's “will” is totally unlike human will. G-d cannot suddenly change His mind. Where humans are subjected to the natural forces (ie, a human's will may be changed due to external factors; for example, if a person is hungry and lacks food he will have no desire to study but be aroused by food, in short, a change in will), Divine will, in contrast, is spontaneous and self-creating. This was how Rambam was able to justify the creation of the world in Genesis 1. It was G-d’s will to create the world. G-d “willed” creation into existence. But G-d's "will" is not subject to natural laws nor external causes, since it is an independent cause (Guide, 2:18).
For the “fear of G-d is the hatred of evil” (Proverbs 8, 13).