I failed to identify whether this is a well-known fallacy, I would appreciate it if someone tells me what this is called.

The fallacy  normally goes like this:

I see you are very happy to criticize the government! Now go back to your place using the road that the government built for you!

So you say capitalism is horrible and must be destroyed - on the iPhone made by a corporation.

You are being an hypocrete criticizing public education because you went to a public school and did your studies thanks to the State, that financed your education

In all cases, the fallacy is assuming that if no public entity had created the environment allowing an individual to do something (or benefit from some advantage), no one else would have.  

If there is no name for this fallacy I would suggest calling it the Christian bridge fallacy. I heard this example from Sam Harris. I don't remember his literal words but it goes like this;

Some historians argue that we must thank the Church for the bridges built in Europe during the Middle Ages. However, this is wrong: the Church built those bridges basically because they were the only ones around with power; if they hadn't done it, someone else would have done it.

In my examples, the same thing applies. I might have been able to study in a public school thanks to the government, but if that weren't the case, I would have probably studied anyway, only in a different way. 

Please notice one important thing too: There might be some cases where this sort of argument is not a fallacy but a real objection.