You're asking about the endosymbiotic theory, which proposes that mitochondria and chloroplasts originated from free-living bacteria that were engulfed by early eukaryotic cells.

Let's break down why some of the following statements would support this theory, and which one wouldn't:

Statements that SUPPORT the endosymbiotic theory:

* Mitochondria and chloroplasts have their own DNA: This DNA is circular, similar to bacterial DNA, and separate from the cell's nuclear DNA.

* Mitochondria and chloroplasts have their own ribosomes: These ribosomes are also more similar to bacterial ribosomes than to the eukaryotic ribosomes found in the cytoplasm.

* Mitochondria and chloroplasts reproduce by binary fission: This is the same method used by bacteria.

* Mitochondria and chloroplasts have double membranes: This suggests they were once independent cells with their own outer membrane, which was then enveloped by the host cell's membrane.

The statement that DOES NOT SUPPORT the endosymbiotic theory:

* Mitochondria and chloroplasts are always found in eukaryotic cells: This statement isn't accurate. While most eukaryotic cells *do* contain mitochondria, some specialized cells like mature red blood cells lack mitochondria.

Explanation:

The absence of mitochondria in some specialized cells doesn't contradict the theory. It simply shows that these cells have adapted to function without mitochondria, which is possible due to their specific role and environment.

In summary, the statement that does not support the endosymbiotic theory is the one that claims mitochondria and chloroplasts are always found in eukaryotic cells. All the other statements provide strong evidence for the theory.