out of interest (& not that it matters, its absolutely your choice) what is your reason for saying no, what don't you like about the idea? I need my drive for my own cars so would never be in that position and not sure how I would feel about it.
I can't speak for OP, but I'd feel the same in her position - unless it was a family member or very good friend (i.e. not one who would feel the need to go over my head and speak to the other adult householder).
I suppose there is the anti-burglar consideration, but it can actually go the other way, if it's a fancy and/or new car and burglars/thieves break into your house specifically to get the keys to 'your' car, to steal it.
If you have an empty drive, you know you've always got a guaranteed space for visitors, tradesmen, deliveries, even the emergency services. You don't have to constantly look at somebody else's car on your own property, which would be weird if they weren't family/good friends - just like you probably wouldn't want your neighbour to dry their washing or store their shed in your garden.
If you or your visitors have young kids, it's somewhere for them to play on bikes or ride-on toys. Unless you have a massive drive, car owners often get used to only having 'just enough' room to walk between the road and their house, as they have to pass the car; why would you not want a clear drive to saunter up and down for the sake of somebody else's car living there? It's easy to forget just how big cars are, when they live outside, but they're actually massive things that take up a huge amount of space - even the small ones - that you could use much better if you're not a car owner.
The neighbour's car could leak oil on the drive, the neighbour might want to wash it regularly in it's regular parking spot. Even with everyday use, it's not just the car standing there, but it's somebody coming on to your property every time they use it, the noise of the engine starting up and doors slamming if they use it at unsocial hours. If the NDN's DD is in the habit of coming and going out with friends late at night, you hear approaching footsteps and maybe chatting on your drive late at night. Some people will sit in their car for a while, whilst it's stationary - making/taking calls, listening to music, doing life admin etc. - all on somebody else's property. It might be a fairly ordinary and inoffensive small car now, but once it's become established that it's her parking space, what if she bought an ugly big old beat-up camper van doer-upper, SORNed it and either left it there and/or expected to keep tinkering with it just outside your window? If you complain, there are tears because they've nowhere else to store it and it's always been their dream to own one, what difference does it make to you as it's only using the same drive as before, you're a nasty unfriendly 'neighbour', nice neighbours do each other favours etc.
In addition, just about any favour ends up being taken for granted if it continues for long. I highly doubt they'd be continually grateful for their kindness in using their drive: no, they'd expect it as the norm. For all you know, they could even complain if it gets into a rough worn state (probably from their use of it) and expect you to repair it, to avoid damaging their tyres!!
I'd hate it - even an empty drive is personal space between the public pavement and your own front door. I certainly wouldn't want to give that up arbitrarily, especially for somebody as rude as him.