Why are chemosynthetic iron and sulfur bacteria thought by some scientists to be the first organisms on earth?

There are several reasons for this, but they mostly have to do with the way these organisms metabolize, and the ecological composition of the early Earth.

Today, the great majority of organisms use aerobic respiration reactions to generate ATP, and those reactions require fuel, typically glucose or some related carbohydrate. In turn, those carbohydrates tend to be synthesized by organisms that can perform photosynthesis. Both of these reactions are fairly complex and have some irreducible aspects which indicate that a highly simplified precursor would not have been as likely as an alternative reaction, such as chemotrophy, which provides much less ATP but is capable of being sustained in anaerobic or nutrient-poor environments, such as thermal vents at the ocean floor, where we observe modern-day organisms metabolizing iron and sulfur in a context analogous to that of the early Earth.

We know from fossil records that the oxygen content of the early Earth was exponentially lower than it is today; the great majority of our free oxygen is actually the result of photosynthetic organisms saturating the crust and atmosphere with it. Therefore, the first life would not have been able to utilize reactions that depended on carbon in order to generate energy. Chemotrophs fit this criteria and therefore seem more likely to have been, or at least more closely resembled, the first life.