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You need to play the game of convincing through going to the social part. This will make things a bit easier and more acceptable to the client. Some customers do not care about the usual wording of quality and price, They want to see more than that.
What you need to do is try to get one of the keys to this person and open that door. These keys are many.
When a customer is acting difficult it is important that you become their partner and not seem like an opponent.
It would be worthwhile to portray that you are as interested in their benefit as much as they are.
Highlight the benefits of your product and also the USP's which would fetch them the said benefits in the long run.
This creates a space for comfortable communication and they will be willing to listen to your offer.
If they still disagree you could make a slightly risky move of withdrawing the offer, the fear of rejection will compel them to rethink the offer and you have higher chances of a closure.