A person cannot see a single cotton thread 100 feet away, but if you wound thousands of threads together into a rope, it would be visible much further away. Is this statement analogous to our DNA extraction

Yes, it is

Explanation:

It is very much analogous. Just as in the analogy explained, DNA isn't visible to the naked eye when it is alone or single, or just one. On the other hand, it is very much easier to see when the DNA are in a cluster, just like in the cotton example.

Succinctly put, the example is analogous to DNA extraction

label a cell membrane

label b cytoplasm

label c ribosomes

label d dna

the membrane forms the outside of the cell

cytoplasm is the liquid within

ribosomes are the components within that distribute rna

the dna is the genetic make-up

not sure if this is what you'r looking for eubacteria and archaebacteria