The shortest answer is, assuming the druid has the best-case scenario available to them, they wouldn't. The scimitar is all-around a better weapon than the sickle, assuming you're proficient in both (since the sickle is simple and the scimitar is martial, this is a reason why a character might wield the sickle instead, but doesn't apply to the druid).
As a general rule of thumb, there is no guarantee that any two weapons on the equipment chart "balance out" against one another (compare the trident and the spear for another sterling example).
That being said, there are some hypothetical reasons why you might find a druid wielding a sickle instead of a scimitar (this list is in no way comprehensive; I'm sure people will add others in the comments):
- Price: a druid who's hard-up for gold might have a sickle because it costs 1 gp. Likely won't be the case for a starting character, but you can run on hard times.
- Weight: the sickle is lighter, so if encumbrance is an issue, you might pack it instead (or as SPavel put it, you might keep a sickle as a backup because you're already weighed down by your main weapon).
- Magic: maybe at some point you find a magic sickle that's better than your plain ol' scimitar.
- Ritual: a sickle is a symbolic item for someone who worships life and nature. maybe for religious reasons, you feel free to use a scimitar to defend yourself but will only use a sickle to deliver the killing blow.
- Tool: besides being a weapon, a sickle is a farming implement. A druid might be caught unawares in a barn and have a sickle in reach. They might be traveling incognito, disguised as a farmer who might be expected to have a sickle but not a "real weapon." They may be out harvesting sacred plants under the full moon when they're attacked by a werewolf, &c.
...all of these are pure speculation, of course, If you're looking for a mechanical/optimization reason why druids in general might carry a sickle instead, refer to my shorter answer :)