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.