Neither of them signed the contract. We don't know why. Perhaps they were uncertain or perhaps THEY WERE VERY BUSY, VERY STRESSED OUT AND RELIED ON WHAT THE OTHER WAS TELLING THEM. You know: verbal contract. Plus the texts in which he said he wanted to help her have a baby. That sort of thing. This 'contract' you are so certain that they signed was between them and the hospital, not between one another. You cannot possibly be naive enough to believe that the lawyer was calling up Jacob and trying to convince him to sign. If Jacob did have doubts before the donation as he now claims, he kept those doubts to himself.
If they relied on what each other was telling them and there was a misunderstanding between the two of them about what the terms were, then there wasn't actually any verbal contract. He thought the terms were one thing and proceeded accordingly and she thought the terms were something else and proceeded accordingly. If they didn't both agree that there was a change made to the terms of their written agreement (and the appeals court which reversed the judge's ruling feels that it's a valid written legal contract between them, so I'll take their judgement of the matter over yours, since it's more likely that they have a better understanding of Illinois law than you do), then the terms of the original contract should remain in force.
The judge made a horrible error by not only ignoring the two contracts in her ruling, but in not even making a ruling on the validity of the second contract one way or the other and that's what the retrial needs to focus on. They have one written agreement and one potential verbal agreement. From what I've seen, there was a lack of agreement between the two about the acceptance of the terms of the verbal contract and that's enough to invalidate it, since a contract which isn't agreed upon by all parties isn't a contract between them.