Yea... "counter-intuitive" is a way to put it softly, been trying to wrap my mind around the logic behind relativity and why it is as it seems to be, to no avail so far. To me it just doesn't make sense.
Relativity is not hard, quantum physics is also not hard either; it all depends on how do we consider matter. If you look at matter as something that has a mass; then it will behave in a way. If you consider it as energetic wave, it will behave in a different way. The fun part is that one entity, could be at the same time both a wave and a body with mass; based on how do you examine it.
The mistake is that in our school, they teach standard physics and then they tell you "btw, forget all that you learned, because there is also this different physics; that is harder to experience unless you go to a particle accelerator laboratory". Physics is probably the only subject that has such inconsistency...math gets more complex, but you don't find cases where you need to wipe your previous knowledge and see at things in a whole different way
We need to think quadrimensionally at this point; beside x, y and z, there is also time, which is a dimension too.