The person you were talking to is correct that the supersonic crack of the bullet is very noticeable. The point of a suppressor is to reduce the muzzle report, thus preserving the hearing of the shooter and masking the position of the shooter.
The sonic crack of the bullet passing gives very little information as to the direction of the shot. The sound of the bullet reflects off nearby objects as well, further masking the direction of the shot.
So while whatever you are shooting at may know it is being shot at, it has no idea what direction the shot came from.
In animals, this results in confusion and the animal generally runs away from the bullet sound, instead of the muzzle report, which ironically can sometimes have them run towards the shooter.
For an enemy soldier, it is clear they are being shot at, but they have no idea where the shot came from, so taking cover is difficult since they don't know what cover is good and what cover leaves them exposed. Instead of an enemy figuring out your location after one shot, it will take many shots to have an idea as to the shooters location and even then it will be a rough guess. By that time there is going to be quite a few wounded.
Take the F-117 for example.
The Iraqis knew they were being bombed in the Gulf War, but they had no idea where the bombs were coming from. If the F-117 was detectable on radar it would have been blown out of the sky. However the stealth of the jet, like the stealth a suppressor provides, masks its position and makes any return fire much less effective.
In Kosovo, through our carelessness and some resourceful intelligence work on the part of the Serbs, they found out where the F-117 was likely going to be and were able to blow it out of the sky with obsolete, though heavily modified, AA weapons.
If you know where something is, then you can destroy it. If you don't know where it is, then it doesn't matter how much firepower you have.