I am trying to make a part move in the workspace with a loop, but the position doesn't change, why?

I wasn't sure if your gate was a model or a part so I showed how to do both:

#If Gate is one part do the following:

To add/subtract from a CFrame's position, you'd want to multiply the current CFrame by another CFrame value. The second CFrame value is amount you want to offset your part.

I changed the name of your position variable to be gateCFrame. The code to move the gateOver would be the following:

adding to position

 gate.CFrame=  gate.CFrame* CFrame.new(Vector3.new(0,1,0))

subtracting from position:

 gate.CFrame=  gate.CFrame* CFrame.new(Vector3.new(0,1,0))

The whole script would be:

detector = script.Parent
gate = game.Workspace.Gate
open = false

detector.MouseClick:Connect(function()
    if open == false then
        detector.MaxActivationDistance = 0
        for i = 1,17 do
            print("moved")
            gate.CFrame=  gate.CFrame* CFrame.new(Vector3.new(0,1,0))
            wait(0.5)
        end
        detector.MaxActivationDistance = 15
        open = true
    else
        detector.MaxActivationDistance = 0
        for i = 1,17 do
            print("moved")
             gate.CFrame=  gate.CFrame* CFrame.new(-Vector3.new(0,1,0))
            wait(0.5)
        end
        open = false
        detector.MaxActivationDistance = 15
    end
end)

#If Gate is a model, do the following: You can't change the cframe of a model directly since models don't have a cframe property. Instead, we need to give gate a primary part by changing the primary part property of the Gate model.

Instead of the above code where we set the CFrame of the gate part, we're going to set the CFrame of the primary part inside of the model. To do that we'd say:

Adding to position:

gate:SetPrimaryPartCFrame(gate.PrimaryPart.CFrame * CFrame.new(Vector3.new(0,1,0)))

Subtracting from position: (make the vector 3 a negative so one is now -1)

gate:SetPrimaryPartCFrame(gate.PrimaryPart.CFrame * CFrame.new(-Vector3.new(0,1,0)))