It would probably be helpful to consider this in context in a good translation.

Using Young's Literal Translation, we find that Paul begins with "Am not I an apostle? am not I free?" and then states all the freedoms and rights he possesses.
 
"4 .... have we not authority to eat and to drink? 5 have we not authority a sister - a wife - to lead about, as also the other apostles, and the brethren of the Lord, and Cephas? 6 or only I and Barnabas, have we not authority - not to work?" and so on.

In other words, Paul had the very same choices everyone has. But he chose not exercise them:

12 .... but we did not use this authority, but all things we bear, that we may give no hindrance to the good news of the Christ."

to dedicate himself to the spread of the Good News. As do priests in the Latin Rite.