That's not really true. You can avoid most if not all government services and still have to pay the same amount as everyone else. They also have a monopoly on most things. It's not like you can go to a competing service.
I disagree that you can avoid using these services, because I don't think that things like public schools are a service only to their direct recipients. Even families that can afford private schools for their children benefit from living in a nation with a high literacy rate. I'm not a 'customer' of my city's social services, but I benefit from having fewer people bottom out and end up on the street.
I don't see the benefit to anyone else to having someone be educated. And if you don't use social services there is no benefit to you (not saying we shouldn't have any, but it's wrong to say they directly benefit you.)
Yes you can go far enough and find "indirect" benefits to anyone for anything, but you have to stretch it quite a bit.
Monopolies are really hard to avoid, which makes your statement seem a bit logically inconsistent. Combine that with the impossibility of avoiding services like military protection, the public education of your community members, the regulation and insurance of the financial markets your money flows through, plus a whole host of other things, and I have a very hard time believing your dream of avoiding government services is in any way attainable.
I wouldn't call any of those things services so much as arbitrary costs. The military is ridiculously larger than it would have to be to offer just defense, education is terrible and they way overspend, and the regulatory system is corrupt and does way more damage than it prevents. Not to mention alternatives for any of these things.
Besides my point is even if a group of people went into the wilderness and declared independence, the government would still go after them and have power over them, even though they aren't consuming any government services at all.