You can be earning money instead of trying to convince this guy why your pricing is justified. If he is happy with sub standard detailing at a lower price, he would never appriciate your work. If he is unhappy with cheaper work, he will call you in the future.
This.
As purely a consumer, I can see where he/she is coming from, especially with something like detailing where you've never dealt with any of the parties involved before. You need to explain why you come in above the competition and justify the added cost. Think of it this way: If you had two products sitting side by side and didn't know much about either, odds are you'd go with the item with the lower price. That is, unless someone saw you pick up the cheaper product and strongly persuaded you to go with the other one.
So you need to decide:
1. How important is the $25? Is it worth losing the job? Do you have others that you can do instead of this one?
2. Why should they pay the extra $25? Explain what you do better than your competition or what you do differently to justify the added expense.
3. Do you see this being more than just a one time job? Or will it be a "one and done" type thing? If it turns into a long term relationship, the $25 is pretty much meaningless. If this is it, then it might be worth fighting for (not literally, of course!)
I can think of a couple approaches you could take.
Try bundling it with a car wash or something else they need and reduce the overall price you would charge by $25. That way they still get the reduction and you get more coin in your pocket.
Lower your price, but explain it is a one time thing to expose them to your excellent services. (Be careful though, this sets a precedence, which is why I would say it is a one time thing!)
Walk away. If they are hassling you over $25, odds are that they'd do it for any of your other future services, unless they see that you did a spectacular job and think the added price is worth it.
Whatever you do, keep it classy/professional. Good luck!