Why do packages of frozen food have printed on them the warning do not refreeze?

Answer 1

The refreeze warning is focused on defrosting, rather than cooking or even slow-thawing them.

If you thaw open at room temperature, with warm water, or in the microwave, the edges and surface, which is where bacteria are probably dormant, warm up first and start to grow.

Refreezing does not kill them, so you have greatly increased risk if you refreeze and thaw the same way, which most people would do.

If you thaw and immediately cook the food, that basically starts you over with a fresh product (cooked <whatever>) that you can safely freeze afterward. Once frozen, the same cautions should apply to this food as well.

If you thaw in the refridgerator, you have less risk, but the food ages(and bacteria etc grow) at the same rate as if it was refridgerated from the start. Most people don't realize this, and treat once-frozen food like it will last longer than not frozen, not realizing it was probably refridgerated before it was frozen and is effectively already older than their fresh food. Since this age is generally unknown, not eating right away is not recommended.