What's wrong with nullable columns in composite primary keys?

Solution 1:

Primary keys are for uniquely identifying rows. This is done by comparing all parts of a key to the input.

Per definition, NULL cannot be part of a successful comparison. Even a comparison to itself (NULL = NULL) will fail. This means a key containing NULL would not work.

Additonally, NULL is allowed in a foreign key, to mark an optional relationship.^(*) Allowing it in the PK as well would break this.

^(*)A word of caution: Having nullable foreign keys is not clean relational database design.

If there are two entities A and B where A can optionally be related to B, the clean solution is to create a resolution table (let's say AB). That table would link A with B: If there is a relationship then it would contain a record, if there isn't then it would not.

Solution 2:

A primary key defines a unique identifier for every row in a table: when a table has a primary key, you have a guranteed way to select any row from it.

A unique constraint does not necessarily identify every row; it just specifies that if a row has values in its columns, then they must be unique. This is not sufficient to uniquely identify every row, which is what a primary key must do.