The first disadvantage, for some, is not having the ability to make big changes. Some places you aren't allowed to even change the color of the paint on the walls. Some like to be able to decorate their place and personalize it. As a renter this is much harder to do.
For some people, there are rules that must be obeyed that you would rather not have to deal with. As a home owner for the most part, you can do what you want in your place. As a renter you will have to respect noise concerns, pet issues, and other things. At times you are even limited to how many guests you can have over.
As a renter you do not get certain tax advantages that buyers get. This means that some of the money you are paying in taxes could have been spent on a mortgage instead based on the way the current tax system works.
You aren't investing in anything as a renter. While home prices can fluctuate and you do lose money in interest, at the end of the month some of that money that you do spend on your home, you do get to keep in the long run. As renter once the money is spent, it is gone forever.
In some renting situations, like living in an apartment, you will have to deal with very close neighbors. This can mean that your sleep could be effected with loud noises and music when you would rather have it be quiet.
Over the long run, your rent payments are going to go up. While there are some things as a buyer that get more expensive, it's a fact that rent over a decade will go up much more than what a home owner is paying.