No, the hadith does not mean Allah loves sin or commands it. It means that human weakness, repentance, and divine forgiveness are part of the wisdom for which Allah created morally responsible beings.
Why the objection sounds serious
The argument is usually put like this: Sahih Muslim reports that the Prophet (PBUH) said if people did not sin, Allah would replace them with people who sin and seek forgiveness. So, the critic says, Allah must positively desire sin. And if He desires it, then He becomes the author of evil while still punishing people for doing what He wanted.
That is a fair concern to raise. If the hadith meant "Allah loves disobedience as disobedience" or "Allah commands people to sin," it would contradict the Quran and the whole moral structure of Islam. But that is not what it says.
"By Him in Whose Hand is my life, if you were not to commit sin, Allah would sweep you out of existence and He would replace you by people who would commit sin and seek forgiveness from Allah, and He would forgive them."
Sahih Muslim 2749
What the hadith actually praises
The hadith does not stop at "people who sin." It says "people who sin and seek forgiveness." The point is not the beauty of sin, but the beauty of repentance, humility, neediness before Allah, and Allah's mercy in forgiving.
A sinless creation already exists: the angels. They obey Allah and do not rebel. Human beings were created with another kind of moral test: knowledge, desire, choice, weakness, accountability, repentance, and return. The hadith is teaching that Allah did not create humans to be angels. He created them to worship Him as humans - and part of that worship is turning back after failure.
This is why the Quran repeatedly condemns sin while opening the door of repentance:
"And Allah does not like corruption."
Quran 2:205
"He does not approve for His servants disbelief. And if you are grateful, He approves it for you."
Quran 39:7
So there is no room to say Allah "approves" of evil in the moral sense. The Quran explicitly denies that.
Allah's decree is not the same as Allah's approval
Classical scholars distinguished between what Allah allows to occur in His universal decree and what He loves and commands in His religion. Many things happen by Allah's permission that He does not love: disbelief, murder, betrayal, oppression. If they could occur outside His power, He would not be God. But if He loved and approved them, He would not be just. Islam affirms neither weakness nor injustice.
Allah may allow a disliked thing because of wise outcomes connected to it: repentance, patience, moral struggle, forgiveness, justice, warning, humility, and the exposure of sincere faith. A doctor may permit a painful treatment without loving pain itself. A judge may allow testimony about a crime without loving crime. Likewise, Allah's creating a world in which sin can occur does not mean He commands sin or loves rebellion.
What this does and does not establish
The hadith establishes that a world of morally responsible humans includes failure and return, and that Allah loves to forgive those who sincerely repent. It also punctures spiritual pride: the believer is not saved by pretending to be flawless, but by worshipping Allah, resisting sin, and returning when he falls.
It does not establish that sin is good, that people are excused for sinning, or that Allah punishes people for something He forced them to do. A person is accountable for the choices he willingly makes, and Allah's knowledge and decree do not cancel human responsibility.
So the strongest reading of the hadith is simple: Allah does not want sin as obedience, virtue, or moral good. He permits a world in which humans can sin because He loves repentance, forgiveness, humility, and sincere return. That is not an attack on divine justice; it is one of the clearest expressions of divine mercy.