If tax money built the parking spot and tax money maintains the parking spot, then why should the government get extra income from the parking spot? Is my tax burden alleviated when I pay to use this parking spot?
It's not a matter of alleviating your tax burden, it's a matter of alleviating everyone else's tax burden so they're not subsidizing your car. You should pay for what you use unless there's a compelling reason for it to be subsidized, not the other way around. Roads are essential for freedom of movement and in any case are too difficult to toll on a massive scale, so it makes sense to subsidize them. Parking spaces are inessential and easy to charge for, so we should charge for them.
Paying to store your car is not a "tax" so it cannot result in being double-taxed. It's a standard payment in exchange for use of property.