Stanza 3 Summary

Get out the microscope, because we’re going through this poem line-by-line.

Up the façades,
his shadow dragging like a photographer's cloth behind him

The Man-Moth begins his climb up the outside of the buildings.
The word "façade" can mean either the facing of the building, or it could mean a false or artificial appearance or attitude. Either of these definitions makes sense, especially when we revisit the ideas in line 13. Perhaps the disapproving faces of the general public are a mask that the people wear to fit in. Our Man-Moth rises above these false pretenses and shows his true self to the world.
His shadow stretches out behind him like the focusing cloth from one of those nifty old cameras.

he climbs fearfully, thinking that this time he will manage
to push his small head through that round clean opening

The Man-Moth is scared, but he's pretty sure that this time he'll be able to make it all the way to the hole in the sky, and he will be able to see what's on the other side.
This is the second time that his fear is mentioned, so it's obviously a very important part of the poem.
Now why would the Man-Moth be so frightened of his endeavor? Is it really the task itself that is frightening him?
The second half of line 19 tells us that he is convinced that this time he will make it, so maybe it's what he will find once he succeeds that is frightening him.
The opening in the sky is round and clean, which contrasts starkly with the cracks and battered moonlight from the first stanza. It's a whole different world up there.
Line 21 gives us a really good reason to believe that the Man-Moth is an artist, since he appears to be imagining himself coming through the hole as if he were squeezed out from a tube of black paint. Maybe you've not squeezed a tube of black paint lately, but how about toothpaste? If you force it out quickly and carelessly enough, it makes a little pile of minty scrolls. (If you've never done this, then just take our word for it because, for all the joy of doing it, it's twice the misery to clean it all up.)

(Man, standing below him, has no such illusions.)

This line reminds us that the Man-Moth is special. Ordinary man does not dream as big or as passionately as the Man-Moth. Of course, the ordinary man is not prone to believing anything except what he has been told to believe, so he doesn't bother to look up and wonder at the moon. Ultimately, line 22 reminds us of what the speaker already discussed in the first stanza because we can't be allowed to get too enamored of the Man-Moth and his world or else we'll forget what our tragic hero is struggling against.

But what the Man-Moth fears most he must do, although
he fails, of course, and falls back scared but quite unhurt.

The Man-Moth's fear is of no consequence in light of his passion.
This last line in the stanza may be one of the saddest in the whole poem. We are led to believe with a simple "of course" that no matter how much the Man-Moth tries, he will always fail at his task. While Man may be a bit of a stick-in-the-mud when it comes to dreams, the truth is that he's just being pragmatic. I mean, really, what kind of whack-a-doodle doesn't believe that the moon is a giant hunk of rock in space but a hole in the sky?
The good news is that the Man-Moth isn't harmed by his failure. He's a little shaken, but he'll just pack it in for the night and try again next time. No biggie.