Is mining the asteroids possible? The short answer is no. While it seems perfectly feasible, it is not possible at this moment due to a number of conflicting factors. These factors guarantee the impossibility of mining the asteroids at the present time, but include a caveat for the possibility later in time.
1. There is too high a cost involved.
It will be extremely expensive to get together all of the equipment needed to mine an asteroid and get it into space. To mine an asteroid, equipment is needed to operate in space. There will need to be a machine to extract the minerals, another to transport them back to earth, spaceships to transport the employees to oversee the operations, and also machinery to convert water to rocket fuel, oxygen and hydrogen if the asteroids should contain water. All of this machinery will be very difficult to build and somehow get into space and placed wanted and needed.
This is a huge limiting factor in the possibility of mining the asteroids for profit. If we do not have the technology to even extract anything from the asteroids and return it to earth, then that is a strong no in answer to the question if mining the asteroids is possible. NASA is currently running a test rocket launch to see if this is indeed feasible. If NASA is not sure that this project is even feasible, then the possibility of it being accomplished is severely limited.
The private company Planetary Resources, Inc. has a lot of well-funded backers behind them and they insist that they have the capability to accomplish this feat by 2020. While this scenario is not impossible, the laws of physics uphold them and Planetary Resources, Inc. certainly has the money, it just does not seem quite possible, at least not in the very near future. So, it's not impossible, but not quite possible either. Maybe there will be a possibility in the future, if not at the present time. So, it has the potential to be possible.
While mining the asteroids for profit is not possible at this time, this does not mean that it will not be possible in the future. It is due to very human and tractable values such as cost and means that it is not possible at this time, not a flaw incompatible with the laws of physics. This means that asteroid mining could very well be possible in the future with reconciliation of costs and improved technologies. The future may very well bring mining of the asteroids for profit or otherwise.