Why not thaw and freeze again?
I have frozen salmon (flash frozen) that I thaw overnight. Because I only eat 3oz potions, there is at least 1-2 potions left that I just keep in refrigerator for 24-48 hours. Each fillet is 6oz so I would have to thaw it fully to make 3oz portions.
Why can't I freeze it again after thawing?
Oh, good lord. Freezing causes the moisture in the cells to expand, breaking down cell walls and structures that provide textural qualities to the item being frozen. Doing it yourself with home equipment maximizes the cell destruction. In short, you get a mushier result. Do it twice and it's mushier still.
Commercial producers strive to minimize cell damage so a piece of frozen fish is often a good substitute for fresh. Once you let it thaw and refreeze you subject the fish to what I described above (and fish is especially susceptible to cell damage from refreezing). You can do it, but you won't be happy with the results.