Be careful, the law isn't every force has an equal but opposite reaction, it's every action. If the action happens to be a force, that just means that what ever apply the force to applies an equal force back on you. You push on the wall, it pushes back on you. Pull on a rope tied to a post and the rope pulls back on you with equal force. In the case of gravity, look at the standard apple-falls-from-tree view that Newton took. The Earth pulls on the apple and the apple pulls back on the Earth with an equal but opposite force. Since the Earth is considerably more massive than the apple, the apple moves but the Earth doesn't (well...not but any measurable amount). And it's also important to not that in general relativity, gravity technically isn't a force. It's just the curvature of space "telling" an object how to move. The object just follows the curve. Not to say a repulsive gravitational force is impossible. Actually, when you start considering things like the electroweak force and the resulting Higgs fields, repulsive gravity is a likely candidate to explain the rapid expansion the Universe that we call the Big Bang. Though I'll agree with what some others have said: be careful not to take the rubber sheet analogy too literally. Objects sink into a rubber sheet due to gravity. You can't really explain gravity WITH gravity. The fact is though that particles cause indentations in spacetime and...well, we really don't know why (or at least I don't know why, I'm not exactly in the loop of current advances in gravitational theory).
edited to add: Beatrix Kiddo, are you saying you believe gravity is exclusively a repulsive force? So, if I bring a particle closer to another particle and they are attracted to each other, are saying this is because the act of bring them together suddenly increases the repulsive force of the rest of the Universe acting on them? I'm sorry, but that doesn't sound like much of a scientifically valid theory to me. Repulsive gravity, if it exists, is an extremely special case that breaks down quickly and in general relativistic terms is a product of an inverted curve in spacetime. The Higgs field specifically define how it would work. And in it's mathematics, such a curve would collapse in a time that would make the blink of an eye seem an eternity. That website you mention is written by someone who seems to be very fond of making himself sound important (he seems to think he deserves credit for a discovery because the word "really" was inserted before the statement) and he admits to having no education in physics and astronomy. All I can say is, be careful what you read.