Can't deal damage to other players

When you hit someone, by left clicking, with a sword or object the other players health should decrease.

When I am left-clicking on another player, on a server, the player does not turn red and the health does not decrease. This is really annoying as games such as Hunger Games are now useless for me as I can never when, because I cannot kill.

I have just bought Minecraft, so I suppose you could say this has always hapopened, and it is not a new thing.