A long time ago it was 7 days before a seller could open a dspute so your rather obnoxious buyer may not know things have changed.

Personally I woukd ignire their emaiks and roceed witht he transaction as I woud any other however if you wan to reply this is what I would say:

I am sorry you feel upset however it is many years since buyers had seven days to pay before an unpaid item disute could be opened, it is now four days and ebay give sellers the ability for this to happen automatically if no payment is received within the first four days.

I am more than happy to allow buyers an extra couple of days if they contact me before bidding or immediately after the item ends as this allows me to exempt them from the automatic process.

I don't know if you buy from overseas but you should keep in mind that sellers on the US site can now open disputes after just two days.

I hope this explains things more clearly