For example, if I buy a copy of or subscribe to the Chicago Tribune, I'm not unjustly "paying twice," just because my tax dollars are paying for a subscription at the public library. It's my choice as to whether I want to obtain my own, personal, private copy. Nobody's forcing me to buy it. I could read it at the library for "free." It's not really free, though. My taxes paid for it.
Same scenario with my own car, house and health insurance. That doesn't mean that I'm paying twice if I drive downtown instead of taking transit. It's my choice.
Many parents choose to obtain private education for their kids. It's not like they don't have a public school option, but what if they also use transit, the public library and the public parks, which I'm paying for but not using on a regular basis? It could be that they are actually using more public services than I am.
The bottom line is: Life would be really crappy if you only used the basic, generic stuff that was provided to you by the government at taxpayer expense, so we all pick our spots on where to voluntarily upgrade our lives from "free" public services by spending our own money for better, private services.
One major reason for paying for private services, instead of accepting public services, is the value of our time. For example, if I wanted to go from my home in Buffalo Grove to any of a number of Chicago suburbs, I generally can get there and back, using the three services of the Regional Transportation Authority (Pace, Metra and CTA). In many cases, however, the round trip would take six to twelve hours, including walking three or more miles, to do by transit what I could do, door to door, by car in 45 minutes to an hour.
I spend more money to do it by private car, but I just don't have the time to screw around being economical and environmental, waiting for multiple connections that are often an hour or two apart and walking a mile-and-a-half, each way, to and from my closest mid-day bus stop and who-knows-how-far from the last connection to and from my destination, while carrying, like a mule, the stuff that I need for the meeting, such as my laptop, my briefcase, my personal items and the stuff that I need for my meeting.
It sure would cost less to use transit for those suburb-to-suburb trips, but I don't have all day to waste, doing in twelve hours by transit what I could do by car in far less time, so I choose to use my car.
Indeed, that's what I have a car, for.
Hey, I could always get a skateboard, but I like to think that I'm a little past that stage in my life. Besides, do you really want to see a 56-year-old guy cruising around town with his left foot on a skateboard and his right foot pushing the sidewalk for propulsion? Wouldn't that be pretty creepy?
Parents who choose parochial schools for their kids, because they think that it is a better value, or because they believe that the school teaches better values, have the right to do so. However, they are not unfairly paying twice. They are voluntarily choosing to upgrade to private services when it comes to education, while they continue to use certain public services that other people don't use because those other people are choosing to upgrade to private on those services.