Why Fluid Speed Increases in the Divergent Portion of a Convergent-Divergent nozzle?

Because the fluid is allowed to expand in the nozzle it increases velocity to fill in the voids created by the shape of the nozzle.

The convergent point of the nozzle acts like a bottleneck trying to slow the fluid and compress it into the reduced crosssection of the nozzle. As it leaves the minimum crosssection it expands into the divergent spaces of the nozzle increasing in velocity as it expands.

++_+

No: it gains velocity through the convergence but in the diverging section, trades velocity for pressure.