Explaining why the image made by a converging lens is upside down is easy -- it really doesn't have anything to do with the lens!
Consider what happens when we have a small hole in an opaque
screen:
Light coming from the various objects travels in a straight line,
with the result that on the viewing screen there are spots of
light that correspond to the objects. The highest object gives
the lowest spot, and so the image is upside down.
This picture also explains why the image is larger when the
lens is farther from the viewing screen.
You can make an image this lensless way, by having a box with a small hole on one side and a viewing screen on the other. This is called a pinhole camera. It has the drawbacks that if the hole is large, the image is fuzzy, while if the hole is small, the image is dim. However, sometimes a pinhole camera is useful, for example to make pictures with x rays, which cannot be focussed by a lens.
The pinhole camera effect occurs all around us every day -- the
disks of light
beneath trees are images of the sun (during partial eclipses
of the sun, they all become crescent shapes)!
You will also see this effect around the house, wherever a sunbeam can enter ththrough a small hole (or a series of small holes, as in this example).
Adding a lens to the camera helps, because converging lenses gather all the light that hits them to come together at the focal point. The result is to get rid of the fuzziness of the pinhole camera image. However, the size and shape and orientation of the picture is the same, because light that hits right at the center of a lens doesn't change direction as it goes through.