That’s just one interpretation of one of the consequences of General Relativity. Looking at it through that lens, the kinetic energy of the object is added to its mass through E=mc^(2). That additional mass makes it more difficult to accelerate it with the same thrust as before so that, when you get to near the speed of light, you need infinite energy to push it over the edge. Because of this, only massless particles are able to actually travel at light speed.
Mind you, this is just one way to look at it, which oversimplifies what’s really going on. I could go on about time dilation and length contraction and Lorentz transformations but that’s a bit beyond the scope of your question.
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