All known organisms are somehow related by carbon chemistry.
Offspring differ from ancestors and the difference increases with the number of generations.
Modern plants and animals have single-celled primitive ancestors.
Alternative suggestions are as follows:
Organisms can arise spontaneously from non-living matter. (Maggots-from-meat hypothesis.)
Organisms produce offspring strictly in their image. (Fixed species hypothesis.)
Similarities are due to basic purposeful design, not common ancestry. (Design hypothesis.)
Fossils have little relevance to understanding the living world. (Playful nature hypothesis.)
Many-celled and single-celled organisms are fundamentally different. (We-are-very-special hypothesis.)
The alternative statements were part of the world-view of naturalists and educated people of the Middle Ages. These assumptions dominated discussions right into the 19th century. They are now abandoned among scientists, but linger in what might be called "folk science". Modern thinking on these matters has merged as a rebellious offspring of the older ideas.
Some of these older ideas are found wanting when tested. Maggots do not arise spontaneously from meat, as Redi showed by screening rotting meat from flies. Also, in breeding different dogs from the same ancestral stock (wolves), the fixed species hypothesis has suffered. (While dogs are still the same species, many of the races cannot breed with each other.) Design, playfulness and speciality are impossible to test and falsify and are not therefore considered scientific hypotheses. To get away from the discussions surrounding such concepts, scientists have changed the rules of the game: much of what passed for science in the Middle Ages is no longer considered a valid object of discussion.
If there is no conceivable test which might show a hypothesis false, it is not science.
Clearly, this ground rule poses some problems for those studying the origin of Life. In a way, such an origin is a "maggots-from-meat" problem, or worse, "maggots-from-inorganic-matter". When Earth first formed from coalescing dust and rocks presumably there was no Life. Sometime later (perhaps 500 million years later) there was Life (we think). Eventually, there were maggots. Thus, we are forced to admit that maggots can arise from lifeless matter after all. It just takes the proper conditions; conditions that no longer exist on the Earth.
The historical sciences (astronomy, geology, biology) have a fundamental problem regarding testing of hypotheses. How would we test the details of an inferred unique event in history? The Big Bang? The appearance of the first cell? The appearance of the first multi-cellular organism? The extinction of the trilobites? When inferred events took place under irreproducible conditions, reconstruction must remain in the realms of speculation. As long as we all understand that we cannot be certain how things happened, we can proceed with building a likely story, a "scenario", based on the best evidence and on known principles of physics and chemistry.
Of course, the absence of certainty regarding the precise course of history in no way strengthens hypotheses regarding purposeful design, playfulness of nature, or a privileged status for humans as a biological species. In analogy with mystery stories: not being sure whether the butler did it in the way proposed does not necessarily implicate the gardener.