The misunderstanding
The owner insures the building, because it belongs to them. They do not insure your furniture, nor damage you might cause. Two policies coexist and do not overlap.
The real exposure
A fire starting in your unit or a water loss can damage the building and neighbouring units. If your fault is established, the sums at stake far exceed the value of your personal property.
What a tenant policy covers
Your property, your civil liability, and your relocation costs if the unit becomes uninhabitable. That last item is the one people forget and the one that gets used soonest.
The figure to watch
The civil liability limit. Moving up a tier usually costs little, yet it is the only amount in the policy that a single event can exceed.
No rate, price, or recommendation on this page. Amounts and limits change: verify them with official sources before deciding.