Monopolies which no one is free to compete against (e.g., the federal government) are corrupt monopolies. They use the force of a gun to force the will and goods of other to serve their own selfish greed. The founding fathers of the United States understood this, and instituted a federal system in which states were not only free, but expected to compete against each other. Unfortunately, those who seek power and control over others and their rights recognized this obstacle, and have gradually coerced and persuaded the populace toward supporting an increasingly larger federal government at the expense of free competition amongst states. No one is legally allowed to compete with the federal government, and thus any endeavor in which it labors who's sole purpose is not to uphold the rights of its people, is corrupt. Both Democrats and Republicans are guilty of this corruption, whether out of malice or negligence is of no importance.
There is no contradiction.
A successful business progressing to the point of an earned "monopoly", is still beholden to both competitors and a free market. It has neither violence nor coercion as means to enforce its interests. However, a government monopoly (note the lack of quotes), retains the privilege to force by means of violence any that refuse its product. If you refuse to pay taxes, you will go to jail. If you refuse to go to jail, you will be forced to go to jail. If you refuse to be forced to go to jail against your life, your life will be taken from you. You are not free in this transaction; there is no nobility in the greed of the government to take what it wants at your expense.
It would serve you well to brush up on the definition of a monopoly, specifically as Webster defines it[1]:
exclusive ownership through legal privilege, command of supply, or concerted action
The important distinction here being "legal privilege". The _federal_ government maintains the sole legal privilege to be the provider of many goods and services which _no other entity is allowed to provide_. Google does not enjoy such a legal privilege and is competing in, please excuse the very loose use of the phrase, a free market.
Please do not co-opt the word monopoly so trivially.
[1] http://www.merriam-webster.com/dictionary/monopoly