Most likely because the seller bought / rented somewhere else to move into, and for whatever reason the new place isn't ready. Or maybe they just couldn't get everything packed in time or couldn't find a moving company. Any number of innocent reasons.
Probably has a buy in place with a 6 month settlement and the date happened to be a week out of whack with your settlement...?
Lining things up...?
Could be plenty of reasons as stated above though....
We had a rent-back seller play games with us about settlement - repeated extensions etc. They were also awful with late payment of rent and with leaving the place in a mess.
Basically, they had some fairly tangled up finances. They weren't going to clear out the whole debt with the sale - they were using part to clear some other debts and keep the rest secured by something else, and they were waiting on bank approval, or something. In other words - in over their heads and robbing Peter to pay Paul (which is why they were renting instead of moving to a new PPOR). And in the course of the lease, we became Peter who was robbed from, too.
As others have said, there are valid reasons for extending and renting back, but take it as a potential red flag. I'd give them the extension, since it doesn't hurt you, but get tough on any late rent payments ASAP. Don't give them any grace. If they are in trouble, make it hard enough for them that they screw over someone else who doesn't push back as much before they start screwing you.
Loss of rental income? Opportunity cost as the new purchase may have their own deadlines in place?
Vendors claim almost double the current interest rates and they keep any incoming rental income.
The world's not a fair place and it doesn't go both ways, but it would be nice if it did.
We recently had a loan that settled late. The vendors agent told the valuer the property was a good development site and the house should be knocked down (his opinion only) and the valuer simply put down land value. They wouldn't review the val so we had to go to a different lender and start from scratch. Neither the vendor nor the agent were too sympathetic to the extra costs incurred by the purchaser.
We had a situation a little while ago where the lady we had purchased the property from actually died during the settlement period so it had to go to probate to sort it all out. The sale went through ok, just took an extra two weeks to transfer the title. The biggest impact for us was that the schedule was out and we had to reorganise our trades that we had lined up to work on the job. Not directly relevant to your situation, but an interesting scenario that can also happen to stretch out the settlement period.