You need to own the animation to be able to play it.
Make sure the animation you are playing belongs to you. Also, your code seems to be a bit off. I'm not sure if it's pastebin, but there's random stuff in there such as "vBig Grinestroy()", and the first bit of your de-equipt animation is inside of the equip animation without anything after it.
another thing, is make sure you're using r15 animations if your characters are r15, r6 if r6 animations.
try running the animation code without any other code so you know that the animation itself is the problem and remember to use your own animations:
local serverStorage = game:GetService("ServerStorage")
local replicatedStorage = game:GetService("ReplicatedStorage")
player = game.Players.LocalPlayer
local newAnim =nil
replicatedStorage.EquipAnimation.OnServerEvent:Connect(function(player,animation)
if(game.Players:FindFirstChild(player.Name) and player.Character)then
newAnim = player.Character.Humanoid:LoadAnimation(animation)
newAnim:Play()
end
end)
replicatedStorage.UnequipAnimation.OnServerEvent:Connect(function(player,animation)
newAnim:Stop()
end)