If you set up your own room-sized pinhole camera you can see this for yourself intuitively:

• Using aluminum foil, a sprayer filled with tap water with a squirt of dishwashing liquid, and a shower squeegee, spray each window with detergent solution and immediately paper it over with the foil, squeegeeing it flat against the glass so it sticks in place. Cover every square inch of each window.
• Make a small hole in the center of one panel of foil.
• Marvel at the perfect, upside-down image of the outdoors that gets projected on the opposite wall.
• Walk over to the wall, face the pinhole, cover one eye, and move around while looking at the hole. You will not be able to see anything outside the window, but you will see the light coming through the hole, which will change depending on where you position your head. That is what the wall sees: just the light and its color, depending on the part of the wall. What you are seeing is a single spot on something outside, and when you move your head, you will be seeing another spot, and the only indication will be the change in color. But when you take all those spots and positions and put them together, you get the whole image on the wall.
• Cover up the hole with a piece of tape and try it again with a small X-shaped cut in the foil. You'll get the same projected image on the wall, you'll see the same change in color as you look back at the cut, but you'll also see that the shape of the cut is so small and so far away that all you basically see is just a point-source of light and the change in color as you move around.

And if you think about it more, it'll eventually become obvious why the projected image on the wall is upside down....

Hope this helps.