Property, or shelter, is one of the first needs on Abraham Maslow's Hierarchy of Needs. These are basic needs which represent a positive development in human life. The lower needs have to be met before one can succeed to a higher level. Having shelter is the step directly after food and clothing.
Owning your own property gives one stability. There are many uncertainties in this world and any of which can affect Landlords. Leases can keep a level of security, although that is not always the case. A property can go into foreclosure. This can, and usually does, negate the lease in residential properties. The new owners do not have to honour the terms and you could be out of your property.
Another scenario can be that the owner needs to occupy the residence for their own reasons. They will have to give you a determined amount of notice and usually some sort of compensation, but you still need to find another place to live. Moving costs you money and most importantly your time. Relocation can also be challenging. Getting groceries, going to school, etc.
I have to point out that there are a few disadvantages. A certain type of personality is like a free bird. They cannot be tied down. They will use every excuse not to be 'stuck' in one place. They just really are free and there is nothing wrong with that. Ownership is not for them. They have a flexible lifestyle and they can easily move their lives to wherever.
In conclusion, there are reasons for each of to own or not own. Weigh them out. I believe that one should always be in ownership of some sort of livable property. The price has to be affordable, of course, but security, safety, and shelter are worth more than money. My advice is to own a property within your comfort level, just own some.