Final answer:
The theory that living cells arose from non-living matter is called abiogenesis, which replaced the outdated notion of spontaneous generation.
Step-by-step explanation:
The theory that living cells arose from non-living matter is known as abiogenesis. This concept is central to the field of biology and relates to the origin of life. Historically, spontaneous generation was a commonly accepted explanation, dating back to Aristotle, who believed that life could arise from non-living material if it contained 'vital heat'. However, spontaneous generation was eventually disproven, and the concept of abiogenesis took its place, suggesting a more scientifically supported process that life began from non-living matter through natural means. Panspermia is another hypothesis that suggests life might have arrived on Earth from extraterrestrial sources, but while it's an interesting proposition, there is no hard evidence to support it.