Put your money where your mouth is

There are 3 people: Taylor, Ellinor, and McGregor. They each have a distinct favorite natural number 1, 2 or 3 and also a distinct Roman numeral $\rm{I}, \rm{II}$ or $\rm{III}$, but not necessarily in that order.

Each person only knew what their favorite numbers are and did not know what the others' favorite numbers are. They each was informed these three facts:

• The person whose favorite natural number is 1 doesn't like the Roman letter $\rm{III}$.

• Exactly one of these three individuals has the same favorite Roman numeral and natural number.

• The person whose favorite Roman number is $\rm{II}$ doesn't like the number 3.

However, none of them are still able to figure out the other people's favorite numbers.

Taylor then makes the claim: "This is ridiculous! These three facts are not helpful at all. I can't determine what everyone's favorite numbers are."

Ellinor (whose first name is Andrew) then shouted: "After Taylor made that claim, I finally knew everyone's number!"

What is Taylor's favorite Roman numeral?

Note: Assume all of them are perfectly logical.

Inspiration.