No, any church doesn't need to explain. However, it's the prerogative of others to critique the statue they turned down and reflect on what they turned down. There's nothing weird about that.
What makes it interesting as well is that the rectors liked this statue very much but admin said no. One tried to find a home for it at another church. I found that to be enlightening as it infers they saw what I see when I look at it.
"Rectors of both cathedrals were enthusiastic about the bronze piece and showed Schmalz possible locations, but higher-ups in the New York and Toronto archdiocese turned it down, he says.
“It was very upsetting because the rectors liked it, but when it got to the administration, people thought it might be too controversial or vague,” he says. He was told “it was not an appropriate image.”
The Toronto archdiocese tried to help him find an alternative location, including St. Augustine’s Seminary in Scarborough. But Schmalz, who describes his work as a visual prayer, wanted to reach a wider, secular audience. “I wanted not only the converted to see it, but also the marginalized. I almost gave up trying to find a place.”
This part is interesting as well, because it's also how I felt when I first saw it.
"When theologian Thomas Reynolds came upon it he felt “the shock of recognition.” He quoted the biblical passage: “ … the Son of Man has nowhere to lay his head.”
I also think that a plaque on the bench quoting Matthew 8:20 would be fitting, as the artist wants others besides the devout to see it, and I think that would help the unfamiliar understand it.