Why wont this script play an animation?

Try using a Local Script.

I'm not the best at animations, but it's probably best to play them from a Local Script.

-- Local Script in tool
local plr = game.Players.LocalPlayer
local char = plr.Character or plr.CharacterAdded:wait()
local humanoid = char:WaitForChild("Humanoid")
local tool = script.Parent
local handle = tool:WaitForChild("Handle")
local swinganim = handle:WaitForChild("swinganim")

function swing()
	local playAnim = humanoid:LoadAnimation(swinganim)
	playAnim:Play()
	wait(2)
	playAnim:Stop() 
end

tool.Activated:connect(swing)-- Edit

Changes I made,

• I used WaitForChild

Using WaitForChild is useful, especially when using a Local Script.

• I used Local Variables

This doesn't really change much, but local variables are more useful and I like the way they look.

• I moved all the variables outside the function

This causes less lag and is overall better. I would suggest getting into the habit of doing this yourself.

• I obviously used a Local Script and used Local Player

This was my guess of the problem.

I hope I helped. If you have any questions fill free to ask me.

Good Luck!

If I helped, please don't forget to accept my answer.