Why can't I specify both a Primary Key and a Unique Constraint on the same table?

You missed a comma after the primary key constraint.

CREATE TABLE [MyTable]
(
    [Id] [int] IDENTITY,
    [Column1] [int] NOT NULL,
    [Column2] [int] NOT NULL

    CONSTRAINT [PK_MyTable_Id] PRIMARY KEY ([Id]),
    CONSTRAINT [UQ_MyTable_Column1_Column2] UNIQUE ([Column1], [Column2])
)

CREATE TABLE [MyTable]
(
    [Id] [int] IDENTITY,
    [Column1] [int] NOT NULL,
    [Column2] [int] NOT NULL

    CONSTRAINT [PK_MyTable_Id] PRIMARY KEY ([Id])

)

  ALTER TABLE [MyTable] ADD CONSTRAINT [UQ_MyTable_Column1_Column2] UNIQUE ([Column1], [Column2])

Or put a comma between the primary key declaration and unique constraint declaration:

CREATE TABLE [MyTable]
(
    [Id] [int] IDENTITY,
    [Column1] [int] NOT NULL,
    [Column2] [int] NOT NULL

    CONSTRAINT [PK_MyTable_Id] PRIMARY KEY ([Id]),
    CONSTRAINT [UQ_MyTable_Column1_Column2] UNIQUE ([Column1], [Column2])
)