I do agree that the concepts of special and general relativity are hard to grasp. To answer your question we need to explore:
- The nature of ‘speed’ (which relates distance with time). It is as simple as it sounds - how fast something goes over time.
- The nature of 'gravity' - not in that it is a force, but it's effect of accelerating objects together
- The concept of relativity and how it relates to gravity
So let's look at the concepts of relativity first. There was substantial confusion century-before-last as to how observational data was not lining up with theories at the time in relation to magnetic fields and classical mechanics. This distilled down essentially to two observable, seemingly (note) contradictory facts:
- light was measured as being a constant speed no matter where measured, or how fast measurements were 'made'
- otherwise 'classical' motion is indistinguishable no matter where, or how fast you are. In other words it makes sense doesn't it that a ball thrown while in a rocket is expected to behave predictably the same as if I was on the ground and threw a ball.
So how can both be true, if the speed of light from a torch on a rocket is measured the same if I am on a rocket, yet when I observe that same light looking at the rocket it should also be the same speed? Previous logic stated that it should be different speeds when measured from different velocities, but they were the same speed. This was the conundrum (simply put - there was a lot of stuff about electric fields and so on, but don't need to get into detail here).
Einstein reconciled these in special relativity, by saying both are true, because in essence observations were that that they were.
He simply then started to think: if they were both true, what else would be true? The difference is really in concepts of time, velocity and distance. So if the speed is of light is the same, it follows on that time must change to accommodate this truth. The rocket must be experiencing slower time to ensure that the speed of the light from the torch is the right speed when measured by someone on the ground. Hence, time and distance dilation occurs when objects are accelerating or decelerating.
Now: general relativity. Einstein had the same truths about gravity. He was likely wondering what gravity is, as concepts of ‘ground’ is also not really defined. Newton said gravity was just a ‘force’ between two masses, however Einstein was dissatisfied with this. If motion and acceleration is relativistic, why not acceleration due to gravity? Surely there shouldn’t be two forms of acceleration out there in the universe…
Hence two postulates for general relativity:
- no matter where you are or how fast you are, special relativity holds true
- including on a planet - where you are experiencing gravity. Ie. there is no difference between gravity and accelerating. Eg. if you are in a rocket, it is the same as if you were on a planet, you are experiencing the same special relativity effects.
So given these two factors - it holds that when you experience gravity it is the same as if you were in a rocket, you experience time and distance dilation as per the previous explanation of special relativity.
NOW THE IMPLICATIONS: Space becomes very weird (or rather just more complicated). Time dilation and distance dilation occur in relation to mass, not just if they were accelerating on rockets. This means light speed from a torch on a rocket is the same speed as measured from a stationary space station (meaning the rocket experiences time dilation) is the same effect as a torch on a planet also (meaning the location on the planet is experiencing time dilation).
This has matched observations, mainly Mercury, which Einstein proved was experiencing slower time close to the sun than when it was further from it, effectively proving the theory of General Relativity.
There is a lot of maths here that is omitted, and this is ‘thought experiment’ realm only, but is the basic principle - which is acceleration causes time dilation (because light is the same speed no matter where measured from), and gravitational acceleration is the same as normal linear acceleration.
Now another aspect of your question of 'why' relativity is true is more philosophical - and calls into question 'why' behaviours we observe are like this and hence the investigations of black holes and so on which push this theory to the limit - and there are still many mysteries to be solved...