If you're open to giving him illustrator credit, you can do that without him taking copyright or using the copyright mark next to his name. You can copyright the completed work to you or your company and still put "Illustrated by Joe Smith" on the cover.
Another reason he may want to retain copyrights is that he may want to use the illustrations in his portfolio. If you have no problem with that, you can grant him a license to do that, with terms you set forth.
If he retains copyrights and you do not enter into a very broad licensing agreement, you may find yourself unable to do things like print a second edition of the book or include it in a collection without his permission.
I guess the issue came up as we are both relatively new to upwork and hadn‘t fully understood the conditions yet. Plus, to my understanding copyright law differs by country and at least for me (and I think also the illustrator) it wasn’t so evident right from the beginning what a (c) really means (economic rights vs right to being named etc.), I assume on Upwork US law applies.
So one learning for me is to next time clarify these things at the beginning of the contract, not at the end!
re: "I assume on Upwork US law applies."
Upwork sets the rules for how things work on Upwork.
If you read about how copyright rules work elsewhere, that doesn't necessarily mean that's how things work on Upwork with regards to who owns intellectual property. Upwork is certainly allowed to set up additional rules beyond that, and require its users to abide by those rules.
For example: U.S. law places no restriction on the number of accounts an individual person may have on a website. But Upwork restricts freelancers to only one account.