Note that none of these characteristics is absolute—with enough pressure change, all phases of matter have measurably varying volumes. And with enough force, all phases of matter have varying shape.
Rather, these are general characteristics that provide guidelines to distinguish solids, liquids, and gases. And these general characteristics are best understood by seeing how they result from the microscopic differences between solids, liquids and gases.
The following is a simplification, but it's an appropriate simplification for a beginning student of chemistry:
Atoms/molecules in solids and liquids are very close together, so they can't be readily compressed. The atoms/molecules in gases are far enough apart that they can be readily compressed—all you're doing is taking up the empty space. Atoms/molecules in solids are rigidly connected. Atoms/molecules in liquids and gases aren't. Thus the shape of solids is fixed, while that of liquids and gases is not.
Now we can ask: What microscopic properties would give you constant shape, but varying volume? Well, in order to have varying volume, you'd need the atoms/molecules to be far apart (like in a gas). This means they're disconnected from each other, and moving approximately independently. If they're disconected from each other, they can't hold a structure, and thus can't have have a fixed shape.
A gas contained within a perfectly uniform spherical balloon could have fixed shape but varying volume as you change the external pressure, but that's a property imposed by the balloon and the surroundings; it's not a property of the gas itself.
Granted, a perfectly uniform solid (a solid whose properties are identical in all directions; the word for this is "isotropic") could have constant shape and varying volume if the pressure around it were increased uniformly, and sufficiently (e.g., let it sink to a sufficient depth within the atmosphere of Jupiter). But then it wouldn't fit into your table, which assumes solids have fixed shapes and volumes.