Buying a home is probably the largest single financial investment you have ever made. For most people, their home is their life savings and most comfortable place in the world.
Could you possibly afford to replace absolutely everything you own? Recovering from even a partial loss, like having your home broken into and many possessions stolen, would cost more than most people could manage on their own. Home insurance protects you from having to pay out a huge amount at once, often at the very worst time emotionally.
Tenants need insurance too. If you don't have insurance, you would be held responsible if your actions (e.g., leaving the bathtub running) caused damage to:
your neighbours' apartment(s)
the apartment building itself
Even if the landlord's or your neighbours' insurance covered the damage claims, their insurance companies would come to you to recover costs for repairs and/or replacement of:
the structure of the building
your neighbours' damaged property
Tenant insurance protects you from having to cover these costs out of your own pocket.