/diy/ - Do It Yourself

We have an issue where if we use something in the kitchen while the dryer is going, both breakers will trip. Here is the current wiring diagram for how everything is set up. I don't know why the home owner decided to do it this way, but it's a complete mess. Is there a reason for tying the neutrals together right away? There doesn't appear to be a reason why two lines are being run to the dryer anyway (it's a gas dryer, so it uses 120V).
I think the double breaker tripping comes from some phase issue with the neutrals. Is there any reason I shouldn't just run two separate lines? They would also finally get a ground line (currently all floating).