"I am weaving a small carpet out of old remnants." - Why does this sentence need the word 'out'?

See a translation

It is similar in meaning to "I am weaving a small carpet USING old remnants." It would be a little different if you said "I am weaving a small carpet of old remnants". Then, "old remnants" would be used to modify the noun (what the carpet is made of rather than what was used to make the carpet)

The original sentence expresses that old remnants are what you used to make the small carpet. It is just how we express what we used to make something.

In retrospect, they both mean the same thing, but have slightly different nuances. (one is used to place emphasis on what was used to make the carpet, and the other is used to place emphasis on what the carpet is like) It is hard to explain, but I hope this helps!