Why is math.random only giving me one response?

This is due to the fact that you're defining your math.random() outside of your function, which means it will always be the same.

Here's an example..

local Random = math.random(1,5)
print(Random)
print(Random)

Returns >> 2 Returns >> 2

Where if we define it inside our function, it'll make a random "value" each time.

function randomNumber()
    return math.random(1,5)
end

print(randomNumber())
print(randomNumber())

Returns >> 4 Returns >> 2

To fix your code do this,

--Finds Player--
local UserInputService = game:GetService("UserInputService")
local Player = game.Players.LocalPlayer 
local Character = Player.Character or Player.CharacterAdded:wait()
local Humanoid = Character:WaitForChild("Humanoid") 


--Finds Animations--
local Animation = Instance.new("Animation") 
Animation.AnimationId = "rbxassetid://2867339187" 
local AnimationR = Instance.new("Animation") 
AnimationR.AnimationId = "rbxassetid://2867339668"
local AnimationL = Instance.new("Animation") 
AnimationL.AnimationId = "rbxassetid://2867395453"
local Animations = {AnimationL,AnimationR}
local track = Humanoid:LoadAnimation(Animation)

--Just finding the Particles--
local particle = Character:WaitForChild("LeftUpperArm"):WaitForChild("ParticleEmitter") 
local particle1 = Character:WaitForChild("RightLowerArm"):WaitForChild("ParticleEmitter") 
local particle2 = Character:WaitForChild("RightUpperLeg"):WaitForChild("ParticleEmitter") 
local particle3 = Character:WaitForChild("UpperTorso"):WaitForChild("ParticleEmitter")
local particle4 = Character:WaitForChild("LowerTorso"):WaitForChild("ParticleEmitter")


--Funtion That Starts Animation and Enables the Particles--
UserInputService.InputBegan:Connect(function(input, proc) 
    if not proc and input.KeyCode == Enum.KeyCode.T then
        local track2 = Humanoid:LoadAnimation(Animations[math.random(#Animations)])
        particle.Enabled = true 
        particle1.Enabled = true
        particle2.Enabled = true 
        particle3.Enabled = true
        particle4.Enabled = true
        track:Play() 
        wait(0.35) 
        track:Stop()
        track2:Play()  --Animaton Follows--
        wait(0.45)
        track2:Stop()
        particle.Enabled = false
        particle1.Enabled = false
        particle2.Enabled = false
        particle3.Enabled = false
        particle4.Enabled = false
    end 
end)

Try using math.randomseed() to randomize the result. It takes a seed as the argument. You can input the current unix timestamp as the seed, as it will never repeat.

math.randomseed(tick())
local track2 = Humanoid:LoadAnimation(Animations[math.random(#Animations)])