However, the fact is many Protestants, if not most, call their clergy "shepherd," since the word "pastor" is a synonym for shepherd.
- mid-13c., "shepherd," also "spiritual guide, shepherd of souls" (late 14c.), from O.Fr. pastur "herdsman, shepherd" (12c.), from L. pastorem (nom. pastor) "shepherd," from pastus, pp. of pascere "to lead to pasture, graze," from PIE base *pa- "to tend, keep, pasture, feed, guard" (see food). The spiritual sense was in Church Latin (cf. Gregory's "Cura Pastoralis"). The verb in the Christian sense is from 1872.
People in the Church are called Shepherds (pastors):
And he gave some apostles, and some prophets, and other some evangelists, and other some pastors [poimenas] and doctors,--Ephesians 4:11
The Lord commands St Peter to be a Shepherd here:
When they had finished breakfast, Jesus said to Simon Peter, “Simon, son of John, do you love me more than these?” He said to him, “Yes, Lord, you know that I love you.” He said to him, “Feed my lambs.” He then said to him a second time, “Simon, son of John, do you love me?” He said to him, “Yes, Lord, you know that I love you.” He said to him, “Tend my sheep.” He said to him the third time, “Simon, son of John, do you love me?” Peter was distressed that he had said to him a third time, “Do you love me?” and he said to him, “Lord, you know everything; you know that I love you.” [Jesus] said to him, “Feed my sheep.--John 21:15-17
Obviously, Jesus is using a metaphor of a shepherd here, telling St Peter to feed His lamb, tend His sheep, and to feed His sheep. So, it is clear St Peter is being called to be a shepherd. It seems to be even more so by the Greek word used by Jesus verse 16 (the second of the three blessings) the word for "tend" is the word poimaine Ποίμαινε, which has the same root as the word for shepherd in Ephesians 4:11, Jesus was literally saying "shepherd my flock."
St Peter commands his fellow clerics to be shepherds too.
Feed the flock of God which is among you, taking the oversight [thereof], not by constraint, but willingly; not for filthy lucre, but of a ready mind-1 Peter 5:2 KJV
The word the KJV translates as feed here is again the Greek for for shepherding, poimanate ποιμάνατε. Meaning, St Peter is commanding them to shepherd.
Two verses later St Peter then calls Christ the Chief Shepherd, now wouldn't this imply that there would be lesser shepherds?
Conclusion: There is no reason to object to the Pope using a title of shepherd, since St Paul used the term for men in the Church (Ephesians 4:11 ie pastors), the Lord Jesus applied it to St Peter John 21:16, and St Peter applied it to clerics (1 Peter 5:2)