Can an “unarmed” attacker be a threat to your life? What is “disparity of force”?

The best answer is to know (in detail) your state's use of deadly force laws.
For example, in NC, we are a "no duty to retreat" and "stand your ground" state. Deadly force is authorized if you reasonably believe that you are in danger of death, grievous bodily injury, or sexual assault. Deadly force is authorized wherever you are legally allowed to be, with no duty to retreat.

"Reasonably believe" is the key phrase, and of course must pass the "reasonable person" test.

In any case, if you carry in any manner (open or concealed) you really should invest in legal insurance. I am and have been a member of the US Concealed Carry Association (USCCA) and I have their Platinum Legal Defense Shield. In short, it guarantees (among other things) an attorney and cash bond should I ever become involved in a self-defense situation, anywhere in the US. I have seen other companies who now offer similar services/insurance. If you carry, protect yourself legally. Even a totally justified shooting can cost you monetarily and legally.

Generally speaking... Yes, an unarmed attacker can be a threat to life and safety. For example, let's say Mike Tyson is acting aggressive toward you. Most people would agree he has the ability to cause serious bodily harm even with his bare hands. Or consider this scenario: A 6', 250lb male is attacking a 5' 2", 105lb female. A reasonable person could infer the female stands a high probability of suffering serious or fatal injury by virtue of the large size differences. Both of these scenarios assume the aggressor is within striking distance and is not retreating.

If it helps, the second scenario is an actual domestic violence case I worked several years ago. The lady suffered permanent disability along with multiple facial fractures, a broken arm, ruptured spleen, bruising to internal organs, and loss of sight in one eye. The suspect used nothing but his fists and feet to hit and stomp. She spent several weeks in the hospital and months of rehabilitation.

Yes you should use force when your life is threatened or another person s life is threatened thats why it is called self defence if you start the fight it's no longer self defence