Why can't a digital camera hold pictures without a memory card?

The memory card is what the digital files are stored on. If you have no memory card in your camera there is nowhere for the camera to store the files. It is like not putting a film in a film camera or trying to burn a CD with no CD inserted to the drive.

No
Some digital cameras have internal memory so you don't need a memory card. I figured this out 2 minutes before I saw this question.