There is a little tool you have to select to scale only the faces from their own center and not the entire object. as shown in these examples.
Right click and hold in the view port choose "object select" in the quick menu. Select your object, then right click hold and go to faces selection. Select the faces you want to scale. Then in the top menu go to Edit Mesh>Transform Component.
(UPDATE THIS IS NOW CALLED SIMPLY TRANSFORM in the menu)
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