The Bible says in 1 Peter 5:1 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; Although he knew tough times were ahead, Peter encourages them to feed the flock that God had entrusted them with. He is simply passing on what he was told by Jesus in John 21:15-17 during his restoration after denying the Lord.
The primary responsibility of the elder is to the feed the flock of God. The apostles said in Acts 6:2 It is not reason that we should leave the word of God, and serve tables. That is why deacons were selected.
Too many elders get sidetracked with other things. I.e. counseling, church administration, etc… These can be snares of the enemy if they are placed on par to or over the primary responsibility of the elder which is to the feed the flock of God. I've seen way too many pastors who are guilty of this.