long oar, sweep
枻 centers on a long oar used to propel or steer a boat, and by extension the sweeping motion of rowing.
枻 combines 木 (tree/wood) with 世, which likely contributes the sound. The character is used for a wooden oar.
The left side is 木 (wood), and the right side is 世 (world/generation). Picture a wooden oar sweeping through the water, moving the boat across the world.
For エイ, imagine an 'A' shaped oar sweeping through the water: 'A' -> エイ, and the wooden oar makes the boat glide.