Forget Flat Earth Theory, now we have Flat Universe Theory!

[Welsh cake]

What is the reason for doubting the infinity of the size of the universe?

Because Infinity is a merely a concept, a numberless expression, and cannot be used to quantify anything. Unlike the universe it is not something demonstrable. Infinity is not a real number or even a real value; it is indefinable as a number so assigning it to anything quantitative or attempting to use it to measure the cosmos is a meaningless exercise.