There's a lot of different arguments. I can't remember them all, but the first one that comes to mind is the hope that legalizing softer drugs would reduce demand for harder, still-illegal drugs. Especially if legalization reduces prices of the softer drugs.

This could be powerful, for example, if we identify that a certain drug is fairly safe but its relatives are not. Legalize the safer form, not the dangerous forms, and market incentives will cause most people to favor the now-legal form. Everybody wins (Though this presumes we have "comparables" to pick between)