The argument goes like this: The hymns are outdated. Nobody talks like that any more, nobody knows what these archaic words refer to, nobody sings melodies like that any more; therefore, the solution is to ditch the hymns and sing only contemporary songs.
But I don't think the reason hymns fell out of favor is because they became old. I think it's because our preaching got new.
The great hymn writers could tell the gospel story with gospel words in very solid ways. But preaching over time became moralistic stories with pop psychology words in wispy ways. We stopped giving the hymns context. We would sing "Oh how marvelous, Oh how wonderful is my Savior's love for me!" but our preacher had long stopped marveling and wondering about the cross, so the song didn't make emotional sense. And then it stopped resonating with us on a Spiritual level.
All good hymns declare the gospel and assume gospel context. I suspect the main reason hymns don't resonate with people much any more is because we don't preach the gospel.
Decline in Popularity of Gospel=Decline in Popularity of Hymns
From Jared Wilson: