Why does a patent not give us the right to use our invention?

With all due respect to Ahmed Alhafidh, a patent does NOT give you ANY rights to use your invention - according to the patent laws, a patent is effectively defensive, not offensive. The rights granted under or by means of a patent is the right to prevent OTHERS from making, using, or selling your patented invention. If you were to practice your own invention, you may be infringing another's patent. So, 1) the purpose of a patent application is to obtain a patent; and 2) once you have the patent, you can then enforce it against others and prevent them from making, using, or selling your patented invention.

There is also an additional scenario which may be of interest to you. Let's say that you are the first one to patent a chair - your main claim broadly recites the chair as comprising at least one leg (a central pedestal), a seat attached to the leg/pedestal, and a back attached to the seat. Now, no one else can manufacture or sell this chair. Someone else comes along and decides that the chair, probably made from wood, metal, or plastic, is uncomfortable, and so they add a seat cushion to your chair and obtain a patent. Having obtained their patent, they cannot make or sell their own chair because they would be infringing your patent - while their chair has a cushion, it also has at least one leg, a seat, and a back - hence they would infringe your patent if they made or sold their chair. But their chair, if it could be made, would probably sell better than your chair because it would be more comfortable. You cannot make or sell a cushioned chair, even though you want to because you can see the comfort advantages, because you would infringe their patent. So, what to do?
You cross-license each other - you can make the cushioned chair, and they can make their own chair because as a result of the license, you have both agreed not to sue each other for infringement. Obviously, this is a very simplistic example but hopefully you can appreciate how patents work.