what is meant by soft handling of a car?

Answer 1

Soft ride, a lot of body roll in turns, car dives under braking, steering a second or two behind steering wheel inputs, all of the traits of those bad old boulevard cruisers America used to make.

Answer 2

When you turn the stearing wheel and it's sort of spongy and loose.

A sports car or high performance car is tight. Though some people like a soft and smooth feel of something like a big Chrysler.