In the Gospel today Peter shows us that to be a Christian leader means constantly accepting the call of Christ to feed and to tend his sheep.
At the end of the day, Peter is a leader not because of his own ability, but because he allows Christ to be his guide and to grant him the grace he needs to persevere.
The same goes for Paul VI whose feast we celebrate today. Paul VI too offers us a vision of leadership which does not rest on power or on personal ability or accomplishments, but which rests on Jesus Christ, the one and the only guide of the Church.
For the daily readings, see the USCCB.