This is part of the European Green Deal. The link isn't clear about it but it's not a new rule that we can't destroy unsold textiles. That rule is from 2024. This is about some finer details and fixes to the 2024 rules.
The 2024 rules are from just before the European Elections, probably in the hope that the unusually red/green European Parliament 2019-2024 (the 9th European Parliament) could get more votes. Von der Leyen also basically had to sell her soul to get enough votes from the red/green parties to get elected, which had a large impact on the way her first Commission operated.
Unfortunately (for them), the 10th European Parliament (the current one) is a lot less red/green. Most member states have also realized that we have a lot of "environmental" regulation that is expensive without helping the environment much (and some cases harming it). We are already in the process of rolling some of it back. Maybe this particular regulation will also be rolled back during the 10th European Parliament.
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The linked page has this text:
"Every year in Europe, an estimated 4-9% of unsold textiles are destroyed before ever being worn. This waste generates around 5.6 million tons of CO2 emissions – almost equal to Sweden’s total net emissions in 2021."
Really? The waste in terms of destroyed unsold textiles generates the same CO₂ emissions as Sweden in 2021? Sweden has a population of around 10 million = a bit more than 2% of the EU (I'm still mentally using the pre-Brexit half a billion number). It has lower CO₂ emissions per capita than most member states due to it having hydropower and nuclear power, but still... call it a round 1% of the total EU CO₂ emissions in round Fermi numbers.
The remaining 91-96% would presumably also generate CO₂ emissions -- 11-20 times as much, in other words roughly 11-20% of the EU CO₂ emissions. Concrete, bricks, heating, agriculture, chemical plants, commuting, etc. all have to share the remaining 80-91%.
I don't think that is very believable.
(A lot of the strangeness comes from using "total net emissions" which allows Sweden's number to go from around 30 million tons to apparently 6-7 million tons. Using the doctored number here makes the textile destruction appear much more wasteful than it really is, especially since the burning of said textiles can easily produce electricity and district heating.)