The correlation between structure and glass formability in glassy systems is a long-standing puzzle. To solve this puzzle, many descriptors based on the short-range order (SRO) have been proposed. Here we show that the SRO, however, offers little help in explaining the glass formability and stability; instead it is the formation of medium-range order that stabilizes the glass against crystallization by suppressing the atomic rearrangement and compositional change. Our results provide a perspective for understanding the correlation between structure and stability in glasses