If there was a legal and binding verbal agreement for you to sell the car to someone else then my next follow up questions would be exactly what were the terms of the verbal agreement, i.e. were any guarantees issued, did you mention that you are selling "voetstoots" etc.
Since you seem to be in a hurry to receive your answer, I have to work with what information I have to try and answer your question.
If you did mention that you are selling the vehicle "voetstoots" or "as is" then the buyer will find it difficult to simply cancel the agreement and you will be able to hold it to him. The "voetstoots" principle will not however help you if there were material defects on the car which you knew about but did not mention to the buyer AND these defects were not visible upon inspection. It will also not help you where defects were deliberately concealed by the seller and effectively hidden from the buyer.
From what you told me the procedure followed by the buyer to try and cancel the agreement was incorrect and can be attacked but this will not help you very much if he can simply rectify some formal requirements and then proceed to cancel the deal in any event.
If you made some guarantees (even verbal boasts) about the condition of the car and it ultimately proved to be false/incorrect, then the buyer is entitled to cancel the deal.
The long and the short of it is that even though it seems as if the buyer is in breach of the agreement, your only way to hold him to the agreement is by taking legal action to force him to go through with the deal. This can take a long time and there is always the risk that the court will find against you (for some reason).
In order to tell how strong your case is will require a detailed consultation with an attorney but from the little that you have told me, you do seem to have a case. Having said that, if I were in your shoes, depending on how easy/difficult it would be to get a new buyer, I would simply accept the cancellation and get a new buyer for the car as litigation is slow and expensive with no guarantees.
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