A written constitution is one whose provisions are formally set down in a single document or a small collection of documents adopted at a specific point in time. Because the framers intend its provisions to endure and not be altered casually, a written constitution almost always prescribes a special, more demanding amendment procedure, such as a two-thirds legislative majority, a national referendum, or ratification by a specified number of sub-national units.
This special amendment procedure is what makes a written constitution rigid. Rigidity in constitutional law does not mean the constitution can never change; it means the process for changing it is deliberately more difficult than the process for passing ordinary legislation.
By contrast, a flexible constitution can be amended through the same procedure used for ordinary laws, as in the United Kingdom, where Parliament can alter constitutional principles by a simple majority. The terms "pliable" and "flexible" both suggest easy amendment, but neither accurately describes the nature of a written constitution. A written constitution cannot be "unwritten" by definition.
The correct association is that written constitutions are always rigid because they require a special procedure to amend.