ELI5: Shouldn’t everyone want to go on the softer tyres during qualification?

I’m a fairly new MotoGP fan and I do certainly not know anything about the technical or mechanical side of things. But I started wondering during Q2 today.

In F1, you want the tyres as soft as possible during qualification because they are the fastest though they wear quicker. Shouldn’t it be the same in MotoGP? There were only a few people out on track with the soft tyre today. I’m guessing there are several other reasons to choose harder over softer or vice versa so I’m wondering if anyone can explain this to me?

I’m a fairly new MotoGP fan and I do certainly not know anything about the technical or mechanical side of things. But I started wondering during Q2 today.In F1, you want the tyres as soft as possible during qualification because they are the fastest though they wear quicker. Shouldn’t it be the same in MotoGP? There were only a few people out on track with the soft tyre today. I’m guessing there are several other reasons to choose harder over softer or vice versa so I’m wondering if anyone can explain this to me? http://ifttt.com/images/no_image_card.png