The analysis table has 3 bands.  When you place a column in the left or right bands, and the bands are visible, the columns in those bands are fixed in position.

Adding a column to a band

Make the left or right band visible by selecting it in the Columns customization window.

You will see an empty row on the far left of the analysis table for the left band.

Drag and drop columns to that area to fix them onto the left of the table.