Brooklyn,
I am going to say, first and foremost, if you do not feel drawn to centering prayer then you should not try it. There may be any of a number of reasons why you might not be called to it. As Joysong noted, you may simply not be ready for it. There is no shame in that as we are all at different points in our journeys and God will call us to what is most appropriate to where we are.
It may equally be that it is just not the right prayer style for your temperment. Different personality types are drawn to different prayer styles. Some prefer rote prayer; others prefer Ignatian prayer; still others prefer an Augustinian or Franciscan prayer style. Any meditative type prayer comes with great difficulty to some personality types, just as rote prayer drives other personality types to distraction. Again, God will draw you toward a good prayer style for you if you listen closely.
As to centering prayer itself, as Jim noted it is primarily based on
The Cloud of Unknowing. But it actually goes back much further and according to the book Prayer and Temperment, by Chester Michael and Marie Norrisey, it was learned by the desert father John Cassian from the monks in the desert. It took on different forms in development, including the Jesus Prayer of the Orthodox. (See pg.25).
There are many people who either have second-hand information from opponents to it, which are primarily based on Frs. Keating and Pennington having visited the East. For some reason this seems to automatically discount them in some eyes, as if Catholics are the only people in the world who pray.

Further, there are indeed many people using centering prayer in ways other than what Fr. Keating teaches through Contemplative Outreach, and many of them are questionable at best. As such, one should certainly look closely at who is teaching this and where they learned it from.
As someone who has been practicing this for several years now, I have personally found it to be of great benefit, though I have to admit that I don’t do it as a regular practice, but use it when it seems the most appropriate way or what I am feeling called to. While most of the time it produces for me a great peace and sense of being loved by God as we gaze at each other, I did have one occasion when God gifted me with interior locutions while I was in that presence. It is certainly not something that one seeks, and is strictly a gift from God, but putting one’s self into His presence would certainly seem to make one more capable of hearing Him should He wish to speak.
As I said at the beginning though, if you do not feel called to it, please don’t try to force it. I say that somewhat selfishly from the standpoint that if you do so and get nothing from it, or have a bad experience, it would then likely cause you to become a witness against it based on that experience when it likely would not be the fault of the prayer at all. Certainly not everyone is called to it, just as not all are called to the rosary as their prayer style. But it is available to those who are called to it; and it is beneficial for those who are called and answer the call.
Peace to you, and my prayers are with you that God will lead you gently where He wants you.