Why can't I blow a fuse?
Thanks to many commentators, I was finally able to blow my fuse.

The main point is, batteries have a significant internal resistance. Hence, they do not provide a "virtually unlimited current". Hence, there weren't enough current to blow the fuse initially.

As Respawned Fluff suggested, I have connected 3 AA batteries in parallel and connected them to the fuse. Connecting the batteries in parallel resulted in a lower total resistance while keeping the voltage the same at the same time, which in turn resulted in an increase in the current. Hence, this had produced sufficient current to fuse the fuse.