The problem with describing the object as moving at the speed of light towards the light is that given relativity, there's no well-defined rest frame for the beam of light. Its a bit hard to describe without invoking math, but basically everyone looking will say that the beam is traveling at the speed of light, but there are lots of possible answers to what speed the object is moving. However, using some math, there are some quantities that everyone can calculate to agree on, such as the "proper time" or "proper length" of that object, which tell us about the rest frame of that object. If they tried to calculate it for the light beam, they would get ridiculous answers like infinity. And thus the rest frame of the beam of light is badly defined.

Simply reversing a statement does not cause any time dilation or length contraction effects. These effects only exist when you say with respect to what other frame you're making the measurements. Different observers in different frames observe different values for time dilation and length contraction. So when doing relativity, you must always define what frame you're doing the calculations in to get physical measurements.

For instance, in your next question you ask about traveling half the speed of light. Note that this must be defined with respect to the earth. If there were another object also moving at half the speed of light away from the earth in the same direction, the two objects would measure no time dilation with respect to each other, but both would measure it for the earth. Given the principle of relativity, the effect of such a time dilation would be 2/Sqrt (3) times the rest frame time. So people on earth see the people on the rocket move that much slower. However, people on the rocket observe people on the earth moving that much slower as well, by relativity. The only time you can find out who aged more is if you turn one around. Otherwise earth sees the rocket as being time dilated slower, and the rocket sees the earth getting time dilated slower in the same way. If the rocket turns around, then there's an acceleration (not just a frame change) that causes the discrepancy in age (people on the rocket age slower). However, if instead we accelerated the earth towards the rocket to catch back up to it, then it's the people on the earth that will age slower than the people on the rocket!