"the [science fiction] writer should be able to convince the reader (and himself) that the wonders he is describing really can come true...and that gets tricky when you take a good, hard look at the world around you."
- Frederik Pohl

Fans aren't sure what Blish was doing in using the greek root "agathos" in this context, since "agathos" means "good". Here's a roundabout explanation, though. Remember that the characters in the novel are talking about a kind of toxin. It turns out that there is a substance called agathic acid that is found in pine needles. Cows that eat too much of these needles sometimes undergo a spontaneous abortion. Agathic acid is an abortifacient; it terminates life. So an anti-agathic - would preserve life? Anyway, nobody knows what Blish really meant.

If you'd like to learn more about it, see this absurdly detailed article at The Oikofuge.

...So I have to throw my hands in the air and acknowledge that Blish just seems to have plain made up some vaguely Greek-sounding names for his anti-death drugs, and evidently didn’t try to keep track of his coinings from one story to the next. But at the time of revision, Blish must have noticed that he’d used three different words in four different stories, and presumably he was aware that he had no sensible etymology to defend even his final choice. He seems to have left us a hint to that effect, in a couple of lines of dialogue he added to the ending of They Shall Have Stars when it was first published in 1956. The lines don’t appear in either of the original short stories that were combined to make the novel:

“[…] Do you also know what an anti-agathic is?”
“No,” Helmuth said. “I don’t even recognize the root of the word.”