First off stealth_nsk is wrong when he says we don't know if combat works the same way in civ 6. We have seen the combat and it is exactly the same system.
Secondly as to why slingers are so bad, as people are saying, or more importantly why is it so much worse than archers, which get 2 range, 15melee combat and 25ranged.
The reason is simple: Due to the way terrain now works, unless things change if a slinger runs back (upon meeting a warrior) onto a forrest/hill/river/rainforest tile: even a warrior with 2 moves can't attack it, even if it moves forward 1 tile, it cannot use its last movement point to charge them.
In civ 5 they could.
In the early game since only Warriors and Slingers exist, it's somewhat fine that they are weaker and need to get up close. If they could shoot over 2 range (which I'm guessing the Civ6 team had tried at some point before nerfing them) then no one would build warriors, you'd have massive armies of slingers moving and shooting everything in sight without taking damage.
Now the next tier introduces a new unit:
Chariots.
This unit gets 2 movenent. BUT if it starts on a flat tile it gets 3 movement. i.e. it can move and then move again onto a forrest/rainforrest/hill tile and kill the archer.
Here the ratio is lowers: A heavy chariot had ~28 combat strength vs. the defence of 15 for archers.
But that is fine since your new units can now chase them.
You will also notice heavy chariots don't require horses: This is because they are a vital part of the combat chain in civ6, without which archers would again rule (moreso than civ5 where they were totally dominant).
So we get chariots < spearmen < archer/warrior, where warriors get +10combat vs spearmen but take dmg, and are less countered by chariots, or you can make archers that can shoot down spearmen without taking damage but are more easily killed by chariots.
Edit:
What does this mean for slingers, are they then terrible?
Well NO, because everyone's example seems to be 1v1, 1 spear vs 1 slinger, or 1 warrior vs 1 slinger. The slinger is better when the number's change, so if you build 2 slingers and your starting warrior, you can kill barbarians without taking so much damage.
I also think slingers were slightly cheaper, and they give the eureka for archers, and they also upgrade to archers for gold not tying up your capital when archers become available.