- Laundering money in poor countries directly hurt the citizens of those countries because the government doesn't collect the taxes it is entitled to
- Most of the money to be laundered comes from illicit activities: drugs, prostitution, human trafficking. I don't have any citations here for proportions, sorry.
Update: fix formatting
Minior nitpick: Poor countries typically have authoritarian, corrupt governments, so keeping money out of their hands is actually a good thing :)
But more to the point: the whole idea of money laundering is that criminals WANT and DO pay taxes on their illegal income by pretending it came from legal sources. If they just kept those money under the mattress they would never pay a penny of taxes, but they also wouldn't be able to actually spend the money. So, money laundering in poor countries actually increases the tax income of their governments.
The western national media has been effective at propagandizing you toward this end. The "typical poor country is corrupt" trope is circulated widely and is used to discredit any attempt at wresting control over a country's fiscal future away from a cohort of wealthy western nations.
Corruption in the west is normalized and simply labeled "lobbying." "Corruption" elsewhere is used as an excuse to overturn elections, topple governments and assassinate leaders.