Ok, so basically anything that has any forces on it will end up with oscillations. On Earth it tends to not matter, because those oscillations travel from the object down into the ground, which is really good at damping them because the ground is, uh, pretty big. Even for things not attached to the ground, the atmosphere inherently damps oscillations, because as objects move back and forth in a fluid, a low pressure zone is created behind the object, which pulls it away from the direction it is moving. Also, rigid objects do much better with oscillations, because the entire structure has to move (more mass moving means less movement when the same amount of force is exerted on it). Floppy objects do worse, because one section can start oscillating on its own without transferring that motion to the entire body.
In space, there is nothing to damp the oscillations. They will just continue without active features of the craft to damp them. If they continue unabated a section may reach a resonant frequency, which can quickly cause failure. Even if it doesn't, those vibrations can cause cyclic loading failures, or just affect the stationkeeping of the craft or it's usefulness in gathering scientific data.
To make a spacecraft resistant to oscillations requires devices like gyroscopes or friction dampers, or long weighted booms which decrease the magnitude of oscillations. Making the craft rigid helps, but the larger it is, the less rigid it will be. And to make it more rigid, or to include more anti-oscillation devices, means more weight. That's an important limiting factor when you need to get the object up into orbit.
One misunderstanding some people have is to think that there are no external forces on free-floating structures. This is untrue. Most importantly, they are all affected by the solar wind, which is a generally constant pressure pushing the object away from the sun. Of course they will also be affected by gravity, and if close enough to the earth they will interact with the atmosphere. (There's not really a clean cutoff to where our atmosphere ends and space begins.) As a result, spacecraft have to perform some amount of stationkeeping maneuvers, which involves applying a force on one section of the craft. That itself will cause further oscillations, because the force can never be transferred perfectly to the entire body. (Imagine pushing a piece of paper in the air with a single finger. Yes, you can get the paper to move in a direction, but you cannot get all segments of the paper to move in exactly the same manner when exerting force at only one point.)
So forces on spacecraft are inherently unavoidable, and oscillations happen any time a force is applied. Oscillations are challenging to control in a free-floating vacuum environment, and become more problematic the larger a craft is. This results in fundamental issues with operating very large spacecraft. That's not to say it is impossible. But in space it's not a simple solution to say "just build it bigger."