Should I stop paying my rent because I'm on holiday for 2 weeks?
It's only analogous if your landlord said you have to move out for 2 weeks because he thinks there is a gas leak even if you don't think there is. Should you pay your rent then?
not pay my car insurance because I decided to get the bus for a week?
Again, if your car insurance company told you that you couldn't drive your car because they thought it was dangerous, even if you knew it wasn't, should you just do as they say amd keep paying them as well?
not pay my mobile phone bill because I left my phone at home?
I hope you can guess how this works now but: If your mobile company cut off your service are refused to let you make any calls, should you keep paying even though you needed to make calls?
of course not, so why is childcare any different
It isn't different, that is the point. If you withdraw a service for no good reason, you can't also expect to be paid for it.
And why do none of you know how an analogy works?