- Nothing happens against Hashem's will.
- Ergo, when one sins, that's also Hashem's will.
- Yet we know that Hashem wants us not to sin, so it's against His will.
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Very short answer: Hashem wants creative beings in His own "Image" more than He wants any particular event.*
So far that's just a paraphrase of Loewian's answer.
We can go one step closer to the ineffable "Mind" of G-d and explore why that would be.
First, the Greatest Good is G-d Himself. Your person who cannot sin isn't receiving that Good, because who he is is compelled by Another. Hashem has total Freedom of Will; being able to enjoy the good of being in His Image would require allowing people at least some freedom of will.
Yes, fewer people would be hurt by others. But the total good in the world would go down.
Second, if we didn't have free will, and we were all automata, would any of the Good He bestows on us be worth anything? Who would be the recipients of his good if humans and grass are only quantitatively different? We needed to be moral agents if Hashem's goal of providing good to others is to be have "others" to be good to.
So, not only would the total good go down, any meaningful definition of good would go down to zero!
* One might argue that the above statement about Hashem's preference is only almost always true. And so the Exodus happening was something Hashem wanted more than Par'oh's being in His Image. Thus Hashem "hardened his heart." The question usually asked, how that was fair to Par'oh to deprive him of a chance to do teshuvah, is a somewhat different one and out of scope.
(**I think "hardened" is a poor translation of either "הכבדתי" or "החזקתי", but that's its own topic. I went with common usage.)
Rambam Hilchot Teshuvah 5:4
ואל תתמה ותאמר היאך יהיה האדם עושה כל מה שיחפוץ ויהיו מעשיו מסורים לו וכי יעשה בעולם דבר שלא ברשות קונו ולא חפצו והכתוב אומר כל אשר חפץ ה' עשה בשמים ובארץ דע שהכל כחפצו יעשה ואף על פי שמעשינו מסורין לנו כיצד כשם שהיוצר חפץ להיות האש והרוח עולים למעלה והמים והארץ יורדים למטה והגלגל סובב בעיגול וכן שאר בריות העולם להיות כמנהגן שחפץ בו ככה חפץ להיות האדם רשותו בידו וכל מעשיו מסורין לו ולא יהיה לו לא כופה ולא מושך אלא הוא מעצמו ובדעתו שנתן לו האל עושה כל שהאדם יכול לעשות
A person should not wonder: How is it possible for one to do whatever he wants and be responsible for his own deeds? - Is it possible for anything to happen in this world without the permission and desire of its Creator as [Psalms 135:6] states: "Whatever God wishes, He has done in the heavens and in the earth?"
One must know that everything is done in accord with His will and, nevertheless, we are responsible for our deeds.
How is this [apparent contradiction] resolved? Just as the Creator desired that [the elements of] fire and wind rise upward and [those of] water and earth descend downward, that the heavenly spheres revolve in a circular orbit, and all the other creations of the world follow the nature which He desired for them, so too, He desired that man have free choice and be responsible for his deeds, without being pulled or forced. Rather, he, on his own initiative, with the knowledge which God has granted him, will do anything that man is able to do.
(Touger translation, my emphasis)
Essentially, then, God's will is that humans have the free choice to act against His will.
I didn't want to go to work this morning. I was tired and wanted to go back to sleep. Yet I put myself in the car and drove here, to work.
Let's try the question with my name rather than Hashem:
I did nothing today against my will.
Ergo, when I drive to work, that's also my will.
Yet we know that I did not want to go to work, so it's against my will. Contradiction?
Can it be that both don't want to go to work, and do want to go to work? Yes. How? Results. Actions have consequences, results. I want the paycheck. I want to have done that which I do not wish to do, because I want the result.
He wants people to choose to follow Him. (Desired result - A paycheck)
To get there, one step in the HOW is giving people choice. (Method - Having a job)
The cost of choice is that some will make undesirable choices. (Cost - getting up, driving)
I want to go to work because I want the paycheck. I don't want to go to work because I'm tired. Being at work is part of my will, and something I'd prefer to avoid, at the same time.
From Rabbi Uri Sherqi:
In short, we are required to abide by what Hashem told us is mutar and assur.
Assumptions 1, and therefore 2, are at least partly false. That nothing happens against the divine will is only true when one looks at the contextual greater picture. But without context i.e. at the "micro" level, choices are made against His will all the time, whenever people sin. He allows this for the same reason that He allows suffering - as part of a larger purpose, primarily free will.
Saying that sin is according to His will is the same as saying that a parent who wants a child to learn to be independent, also wants the failures and suffering that inevitably result.
I'll try an answer as well - I think the other answers have been converging on the same idea.
Short answer: #3 is a false statement.
Longer answer : The premise ("Hashem wants us not to sin") does not imply the conclusion ("sinning is against His will"). This is because, as has been alluded to by the other answers, the "wants not to sin" refers to the ultimate/overall G-d's desire of us choosing the right thing [this is the פנימיות הרצון]. So the word "want" in the premise does not refer to the same the same concept as the word "will" in he conclusion - the latter being the desire of G-d according to which all events happen [חיצוניות הרצון], which is assumption #1.
In other words, to realize the ultimate/long term desire of man doing good ("G-d wants us not to sin"), sinning is allowed to exist (i.e. it is according to His will).
Many years ago I read a book called Atlas Shrugged. (Not a recommendation, just credit.) From it came a quote that has helped me a great deal in studying the OT in Hebrew. (non-Jew, former agnostic)
"Contradictions do not exist. Whenever you think you are facing a contradiction, check your premises. You will find that one of them is wrong."
I only use the phrase today of 'pseudo-contradiction' when seeking help from others to find the right pieces.
What was the event that brought death/sin/chaos into the world, according to Genesis? Disobedience.
As above, so below.
In the beginning, Elohim created/'birthed' an Entity. It was not Elohim's desire to father a child from this Entity for a time. The Entity willed to create without a consort/proper consort, and a fearsome/evil/lacking child was produced.
Elohim had created the Entity with Free Will. Elohim did not create Evil, but allowed the exercise of Free Will to bring Evil into the Heavens.
Elohim is Love. He did not purpose to leave the Heavens in such a dismal state; He had a plan - and we are It. Microcosm of the Macrocosm. Correcting from the bottom up, so to speak.
I offer this as the tool I found to get through a hurdle that once baffled me (and countless others). It was found in other ancient texts, and then opened my thinking in such a way as to see the application unfolding in the Hebrew OT.
Why does G-d allow evil?
Maimonides states: 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).
The Babylonian Talmud (Berakhot 61a) explains: there are two letters yud in the Hebrew vayyitzer, “and He created” in Genesis 2:7. This denotes the existence of a yetzer ha’ra, an evil inclination, and a yetzer ha’tov, a good inclination.
Why were humans given the ability to do evil?
Perhaps it is G-d's will. In Hebrew sin is cheit or hamartia in Greek, which means "misstep" or “missing the mark," as if one is shooting an arrow and misses their target, hitting the outer rims instead of its center. What do we do when we shoot arrows and miss our targets? Do we cry, pound our chests, and ask forgiveness on special holidays? No. We reach into our bag or quiver, where an archer keeps his arrows, and attempt to aim again. Perceiving sin in this perspective, we find that we can learn from sin.
For example, if you work at the gym your muscles are going to ache the next day, but it is a good feeling, for that pain is an indication that your efforts are finally paying off. There is a saying "no pain, no gain." Thus, sin, in this way, is a learning process.