You gave up.
In German “das Handtuch werfen” literally “throwing the towel” for giving up.
This comes from boxing where the corner man will throw a towel in the ring if he thinks his boxer is no longer capable of fighting.
But why do Italians throw a sponge? Yes, the corner man usually has also a sponge but I have never seen it thrown.
Maybe I can use the expression at home if I am no longer capable of dishwashing.
Edit: I have to correct myself. According to Collins in English you can also “throw in the sponge”, indeed again related to boxing. Never heard it.
Ciao. This is one of my favourite expressions learnt from the lovely Simone “Italiano in 7 minuti”. In GB we also throw in the towel and tbh I’ve never thought to ask why Italians throw in the sponge. Good luck with avoiding the dish-washing;-)
Buona giornata a te!
Edit: I actually threw in la spugna with Cloze’s “Speaking” option but today found il coraggio di fare the dreaded Updates. Allora I can now Speak on the app and it’s great, I’ve really missed being able to use this option. Allora, devo trovare il coraggio di fare Updates for my web version which will inevitably solve that problem!