Line of code that would make an action ignore the player who starts it?

Not sure how to phrase this answer but when you're creating the AOE attack pass it the name of the player who cast the spell as an argument and then don't apply the spell to them, for example:

local player = game:GetService("Players").LocalPlayer

local function castAreaSpell(caster)
    -- create a part to act as the Area Of Effect (AOE)
    local area = Instance.new("Part")
    area.Size = Vector3.new(20, 20, 20)
    area.Anchored = true
    area.Position = player.Character.HumanoidRootPart.Position
    area.Parent = game.Workspace

    -- get all parts within the AOE,
    -- if the part is the child of a player character,
    -- add it to table touchingChars
    local touchingParts, touchingChars = area:GetTouchingParts(), {}
    for _, part in pairs(touchingParts) do
        if game:GetService("Players"):GetPlayerFromCharacter(part.Parent) and not touchingChars[part.Parent] then
            touchingChars[part.Parent] = true
        end
    end

    -- loop through all the chars in touchingChars
    -- and apply effect of spell as long as the char is not the spell caster
    for _, char in pairs(touchingChars) do
        if not char.Name == caster.Name then
            -- apply effect of spell
        end
    end

    -- clean up the mess
    area:Destroy()
end