Why does the DMA get priority over CPU when both request memory transfer?

The DMA controller gets priority over the CPU for the memory bus because an I/O device cannot wait. A device such as a disk delivers data at a fixed speed. If its word is not moved at once, the next word overwrites it and data is lost.

The CPU, on the other hand, can be delayed for a cycle without any harm. It only runs a little slower. Hence the memory cycle goes to the DMA controller first, which also keeps the high speed device working at full rate.