Working out with free weights stimulates both your prime mover and stabilizer muscles. That is, you need strength in your arms and legs and chest/back (i.e., prime movers) in order to move the weight, but you also need strength in your abdominals, mid-spine, and smaller muscles surrounding the joints (i.e., stabilizers) to hold correct positioning to enable safe and efficient movement patterns.
Compare this against machine based strength exercises. Yes, strength can be developed in the prime mover muscles but the rigid steel bars of the machine remove the need of your body to stabilize itself, and thus your stabilizer muscles aren’t adequately strengthened.
So, why should you also strengthen your stabilizer muscles? Because the demands of an everyday active life — running, jumping, picking up things, playing sports, or being active with your kids — require it; there isn’t a metal exoskeleton to stabilize your body outside the gym. At least not yet.