I'm listening to the 'Norman Centuries' podcast by Lars Brownworth, and in one of the episodes it is mentioned that vassals of Normandy began to build unauthorized castles, weakening the central government of the Duchy. Why did this weaken the central government? Why was it such a big problem to have unapproved castles in the medieval era?
Well, basically a castle is something difficult to take (or storm), is a fortress and is expensive. So the simplified process is something like this:
What is the meaning of this? It means that somebody needs funds to build such structure so this person is already somebody powerful, once built the castle becomes a stronghold and becomes very difficult, lengthily and costly) to dislodge the defenders or take it by assault or siege.
By its very nature castles are built in advantageous and strategic positions so they dominate over an important portion of land and hence create a sphere of influence, peasants, farmers, monks etc will gravitate to the castle, the castle will also have a garrison or some sort of small army and village or villages are likely to appear around the castle and eventually all these souls will pay tribute and become subjects of the castle owner, he provides a court of justice, etc and so he becomes a Lord himself hence eroding the central government as you point out in your question. So in few years Mr King or Duke XYZ has lost a county or a region to another noble.