Because once an AI becomes proficient at formalized logic, it:

1. Completely stops hallucinating, since we can demand it to internally prove its claims before showing the answer;

2. Stops outputting incorrect code (for the same reason);

3. Starts being capable of outputting complete projects (since it will now be able to compose pieces into a larger code);

4. This is also what is needed for an AI to start self-improving (as it will now be able to construct better architectures, in a loop).

That's why I argue getting the AI competent in logical reasoning is the most important priority, and we'll have no AGI until it does. After all, humans are perfectly capable of learning how to use a proof assistant.

Moreover, if an AI can't learn it no matter how hard it tries, you can argue that there is at least one human capability that the AI can't replicate, thus it isn't an AGI.