How did round planets form from the explosion of the Big Bang?

I thin that what he means is that even though your choice is evidence-based, it remains a choice in the sense that you decide that you have enough evidence to put your confidence in a given theory. The point where you decide you have enough evidence could be viewed as a choice, although probably unconsciously in some/most cases.

Isn't the universe considered infinite and Euclidian in the BBT ? I'd hope you could clarify this little bit because it seems very counter-intuitive to my understanding of it.

I asked the question because I would think physicists would say 'visible universe' when they wanted to talk about the visible universe, and univers when they wanted to refer to the universe. Hence my question, if the universe is supposedly Euclidian (therefore infinite), then how can you measure it's size ?Or did he simply mean observable universe ?