I know that in the middle ages across much of Europe war consisted less of a series of battles as a series of sieges. Defenders were rarely keen on open battle unless forced or strongly in their favour.
It's a general assumption that castles had to be taken, or at least invested. Perhaps the answers are obvious, but my question is exactly why this had to be done?
Given that garrisons were generally fairly small compared to armies, what trouble would they cause if left behind? (Assumption here: how large were garrisons when reinforced in wartime?) How did a castle control the space around it? Purely by physical position (eg. right next to an important road or town)? Or by allowing a defender to project small forces to difficult places, disrupting lines of communication, etc.?
What examples do we have of castles and their garrisons causing problems for invaders after being bypassed or breaking out?
Related question: to what extent was the taking of castles symbolic, a sign of success rather than a more tangible military benefit?
Both pitched battles and sieges were comparatively rare and risky in Medieval warfare, compared to raiding. John France makes the case in Western Warfare in the Age of the Crusades 1000-1300 that sieges could be regarded as, in many ways, an extended form of battle, with both being high-risk gambits that commanders preferred to avoid and risked causing the army to disintegrate.
Suppose you're the leader of some invading army. You take the surrounding countryside, but not the castle.
Now, suppose the hostile castle garrison strikes out at some undefended part of the countryside on a raid, stealing cattle and other reasonably portable valuables, both because they need it and to hinder your operations. Even a small force could do some damage when raiding largely undefended targets.
How do you stop that? You could defend the sources of wealth themselves -- the villages and such -- but they're widely dispersed. If you defend one strongly, they'll pick a different one. If you try to defend them all, you don't have the resources.
Alright. So you don't know their destination on raids, but you know where they start: the castle. It makes more sense, then, to intercept them at the start of their journey rather than the end, right? So you defend against them right at the gates.
Once you're defending against a potential raid from the castle at the castle gates, though, you're already 90% of the way to laying siege. All you need to do is deny them provisions, and you are besieging them in practice.
In short, even a small group of armed soldiers to cause some amount of havoc if they're allowed to go out, plunder and burn things, and retreat to their fortified refuge. In fact, Raymond of St. Gilles, from 1103-1109, was able to ultimately compel Tripoli to surrender by raiding its supplies from behind the safety of a nearby castle.