Yes and no?
To the first part of your ask: Yes, the manga explains why Furuta wants it. When he’s dying, Furuta confesses that the one thing he really, truly yearned for in life was a family; namely, Rize and their children. Since pregnancy is required for biological children, I’m guessing that’s why he wanted to impregnate her.
But for the second part of your ask…why does he specifically mention his fear that she would become pregnant?
The manga doesn’t explicitly cover this. But IMO, there are three prominent possibilities:
1. I mean, Furuta’s jealousy is canon. His entire dream was to have happy kids with Rize as his wife, so I’m sure he hated the idea of her sleeping with anyone who wasn’t him, and especially having their baby.
2. He’s also a Washuu, raised in a literal rape garden. I’m guessing he has some pretty misogynistic ideas stemming from that upbringing. So the idea of Rize being ‘ruined’ if she had sex/got pregnant might also have upset him.
3. There’s also a third (slightly more noble?) theory, which is that if Rize had had a child, she would have been a ‘breeder’ anyhow, even if not in captivity. And a child in tow would probably render her easier to capture.
Furuta expresses frustration that Rize didn’t appreciate his sacrifice in freeing her – he probably means his romantic feelings, but he could also mean the ways her reckless behavior nearly resulted in her capture, over and over. Perhaps he felt like Rize was wasting his sacrifice (since his relationship with his father is strongly implied to have deteriorated around that time).
Personally, I think it’s a combination of all three, but primarily the first two. 
Feel free to tell me what *you* think.
Mercy and Magic 