A.D.
He's developed a phobia, which is not that uncommon with children at his age. it's an intense fear, which is very real to him. He can't control himself because he doesn't know how to. You can't reason or use logic with him to help him, nor can you take a heavy-handed approach with threats and consequences. You're going to have to work with a child therapist to guide you as you both learn the way to work through it. It is frustrating, but It will get better.
My youngest child at 4 developed an intense fear that flushing the toilet would flood the bathroom, and the house. We're talking screaming, shaking, crying, tantrum fear. We were exhausted trying to force her to get over it. Finally, a family friend that has a background in child development told me it was ok for us to tell that we have decided to help her by flushing for her until she learns to feel comfortable doing it herself. After a few months, she started flushing again. We only brought it up several months later when her older sister and cousin were going to see the movie "Flushed Away" She wanted to go, and we told her we didn't think she should go because it may upset her. After a few months of us not "forcing" her to flush, and not having crying fits of anxiety, she then decided to try flushing again. And asked us if she could go to the movie because she was ready to try. This was her idea, we didn't set this up. So we said OK, and she did it. Well, she did it standing on the bathtub and reaching over to flush, but that was a big step. It all got better when we let go of the fight and accepted it would take her time to for her fear to subside.
I'm not sure how that translates to working through a fear of bugs since you can't really control when one may see a fly or ant, so I would talk to a child development expert to figure out the best strategy with him