Which theory explains why mitochondria carry their own circular DNA?

Endosymbiosis - the proposal that mitochondria were once free-living bacteria engulfed by another cell and never digested. The evidence is hard to argue with: they have their own circular genome like a bacterium, their own ribosomes of bacterial type, a double membrane, and they divide by splitting rather than being built by the cell.

Lynn Margulis published the argument in 1967 after rejection by about fifteen journals, and it was ridiculed for a decade before becoming textbook orthodoxy. Chloroplasts have the same origin from cyanobacteria, which means the two things that make complex life possible - respiration and photosynthesis - are both captured organisms.

The merger explains a peculiarity of inheritance. Mitochondria come almost entirely from the egg, so mitochondrial DNA passes down the maternal line alone and does not recombine, which makes it a clock for tracing ancestry - the basis of Mitochondrial Eve, the most recent woman from whom everyone alive descends in an unbroken female line, who was not the only woman of her time and is a statistical artefact of lineage rather than a first mother. Margulis went on to argue for symbiosis as a general engine of evolution, a broader claim that has not been accepted.