It will not print or kill my player, where did I go wrong?

The problem with your code was that the Region you had created at line 1 was not the same Position as the hitbox part you had created on line 3.

I tried creating objects for the Min and Max Vector for the region. That resulted both of them being outside of the hitbox part.

You're now not required to having a hitbox part. You're now defining the Position, and Size as a variable at the top.

You're free to remove the code from line 12 to line 18 if you want to. It'll only provide you a means of debugging.

-- Services
local playersService = game:GetService("Players")

local sizeX, sizeY, sizeZ = 10, 10, 10
local hitboxPosition = Vector3.new(0, 5, 0)

local upperCorner = hitboxPosition + Vector3.new(sizeX/2, sizeY/2, sizeZ/2)
local lowerCorner = hitboxPosition - Vector3.new(sizeX/2, sizeY/2, sizeZ/2)

local region = Region3.new(lowerCorner, upperCorner)

local hitbox = Instance.new("Part")
hitbox.Parent = workspace
hitbox.Anchored = true
hitbox.Size = region.Size
hitbox.CFrame = region.CFrame
hitbox.CanCollide = false
hitbox.Transparency = 0.75

while true do
    local partsInRegion = workspace:FindPartsInRegion3(region, nil, math.huge)
    for _, part in pairs(partsInRegion) do
		local player = playersService:GetPlayerFromCharacter(part.Parent)
        if player then
            local character = part.Parent
			local humanoid = character:FindFirstChild("Humanoid")
            humanoid:TakeDamage(humanoid.MaxHealth)
        end
    end
	wait()
end