The context. Let's see what group is comparing himself with:
1Co 9:1, 5, 12 KJV - (1) Am I not an
apostle? am I not free?
have I not seen Jesus Christ our Lord? are not ye my work in the Lord? ... (5) Have we not power to lead about a sister, a wife,
as well as other apostles, and [as] the brethren of the Lord, and Cephas? ... (12)
If others be partakers of [this] power over you, [are] not we rather? Nevertheless we have not used this power; but suffer all things, lest we should hinder the gospel of Christ.
Clear?
Also, what right is he talking about?
Jesus taught that the people of the city you are going into to start congregations should voluntarily support you while you are there evangelizing:
Luk 9:2-4,
Luk 10:3-9, (also in Matt, and Mar).
Notice this interesting part:
Luk 10:7 NKJV - (7) "And remain in the same house, eating and drinking such things
as they give, for the laborer is worthy of his wages. Do not go from house to house.
That was a lesson for them to show them how to do it at that time. They would go, the people of the city responding to the message should financially help them, but it was "as they give". The interesting thing was that their first experience doing so was in the cities of Israel, so they definitely couldn't go around saying "I'm your new levites, gives all your tithes to me" LOL.
Anyways,
That's what apostles did:
Peter staying with Simon tanner while ministrying in Joppa:
Act 9:43
Paul stayed with Lydia, a new believer, while he preached in the area:
Act 16:14-15
Now, this is what happened in Corinth:
Paul stayed with Aquila and Priscilla, while he reasoned in the synagogue every Sabbath, and worked as a tentmaker:
Acts 18:1-4
Then, he moved to Justus's house, who lived beside the synagogue, who was a new believer, for one year and six months while he taught:
Act 18:6-11.
But apparently, according to 1 Corinthians, he didn't stop working as a tentmaker, while he could have.
Does everything make sense now in Context? That's Paul's point in 1 Corinthians. We don't have to put into the text more meaning extrapolating it into "bishops".
Now, many Pastors that are sent to a town, are in reality evangelist, trying to start a church. It is a lot of work at the beginning. I see nothing wrong with locals and also other churches supporting him to go as full time as they can.
Also, I see no problem with supporting pastors that are trying to go full time as Bible teachers because there is a huge demand for ministry training.
In general, I see no problem with supporting certain individuals full time for ministry as long as what they are doing has to do with missionary work locally, or training many others for missionary work; as long as it is from voluntary offering, without coercion.
If the pastor is just being a "catholic priest", it is like, meh, no point.
But, there is also the principle of blessing those that teach you, which does not need to be a salary, but you can bless them in many ways.
Gal 6:6 Let him who is taught the word share in all good things with him who teaches.