Why is only the speed of light constant in all frames of reference?

To answer this question, one needs to answer, what do mean by why? What's the intention to ask. One can ask why solid is solid, or liquid is liquid. For light, it is made up of photons, which has zero rest mass. At the time of origin of the universe, photons were there.

Somehow, the world has a cosmic speed limit, and any particle which can have that limit is massless. So, any object which has mass zero or says particle moves with the speed of light.

Another example is a graviton or gravitational waves. So, light happens to be one of the particles which mass is zero. And in every inertial frame, this cosmic limit must be the same. It can't be different. Note, I have said any inertial frame. I am not talking about the non-inertial frame.

According to the later well defined 2nd postulate of the particular theory of relativity (by Sir Albert Einstein), speed of light is constant in every inertial frame of reference. You will come across it more vividly once you learn about the Lorentz Transformations and Minkowski Flat space. But for the time being, you get the idea of it.

3 × 10^8 m/s whatever might be the speed of object irrespective of the frame. Eg.: You are standing and looking at a ray of light, as you are stationary w.r.t. The surroundings you find the speed of light is 3 × 10^8m/s. Now if an alien from its spaceship looks at you, you are moving as the earth is revolving and rotating. So you have a speed due to that frame, but still when that alien looks at same light ray. The speed is always the same. Now alien tries to catch the light ray and boost the engine of its spaceship, and still, it sees the same the light ray is still going with the same speed, the person standing on the ground looks at this eye-catching moment, and he still considers that speed of light to be constant.

The first thing you need to understand is, what is the speed of light. In Newton's world of physics, speed of signal was referred to be the speed of light, but in those times space and time were discrete quantities. Because of that, the speed of signal was assumed to be an undetermined quantity. Later, Einstein came into the picture and intricated the idea of space and time, and by the Michelson Morley Experiment, speed of light was found to be constant. In that experiment, Earth's velocity was tried to measure relative to the medium aether as proposed by Maxwell.

Although Maxwell defined the speed of propagation of EM waves to be 'c', he thought that it is relative to the non-existing medium aether. The idea of aether dates back to times of Christian Huygens.