Here is how I see it, and I am not specifically discussing infallibility, as that is another issue in my mind.
Either Peter had primacy or he did not. If he did, then is it logical that apostles after him also have one who has primacy over the rest? If so, what does that primacy intail?
Now, my answer to the first question is "Yes. Peter did have Primacy over the 12. It was not just an honorary thing, from my reading of Scriptures.’
The second question would be asnwered “Yes, if Chirst set the Church up in that manner, it makes sense that the Bishops, who are the holders of Apostolic postions, would also have one with Primacy over the others.”
The third question, in my mind, is answered thusly “This primacy is represented as one Bishop having authority over others in matter of the day-to-day opporations of the CHurch. I can also accept one as overseeing the teaching of Doctrine and, when needed, calling Councils.”
You can call it suprimacy if you want, though I see the two as being different. Infallability is another issue.