Freaky, but true.
Not sure what you mean by relative time?
It is not logical if you really believe that speeds add linearly (that is, if you are going 5mph past an observer and throw a ball 5mph, that the result is the ball moving 10mph).
Speeds don’t actually add linearly like that, but they come very very very very close to doing so for all speeds humans are used to dealing with.
So, we all have very deeply held gut feelings that speeds should add linearly. Once you let go of that, it becomes much easier to understand many of the things that don’t feel logical about relativity.
Ultimately, it is logical, but from a different set of axioms than most humans tend to have.
We just don't realize we live in a 4D space where time is one dimension, so we think driving in opposite directions is a special case where we can add the speeds. but there is the fourth dimension, and we have to use an equation very similar to Pythagoras to get the right value.
I know you must know this, this is more for the benefit of the reader.
I wrote a long answer to someone else; I'm not going to retype it. But what is invariant in the 3D space you think you live in is distances. The distance of you from the kitchen is computed to be 8 meters no matter what we choose to say the x and y directions are, right? If we choose different directions for y, you may say the kitchen is 6 meters from you in the y direction, I say it is 3.7 meters in the y direction. No mystery, our frames are rotated. But we both get the same value for distances. Rotating a map doesn't change the reality of how far you are from the kitchen.
Well, you don't actually live in 3D space, you live in 4D space, where time is a dimension. So what is invariant is not distance (3 of the 4 dimensions), but intervals (time and distance between two events). when you travel at a significant fraction of light speed, you are rotating that 4D 'map'. If you rotate frames, you get different values for x, y, z, and t. But the intervals are still constant.
The intervals are the same for all observers. It is just the individual coordinates (x,y,z,t) that vary for different observers, just like (x,y) are different for you and me wrt your kitchen, but the distance we compute are the same.
edit: in summary, wouldn't you find it bizarre if I rotated the floor plan to your house and suddenly got a different distance from your couch to the kitchen? That would be absurd! Well, when you rotate in space time intervals are unchanged. IOW, the speed of light is unchanged. It would be bizarre if by a simple rotation you got a different value! You just don't 'see' (literally and figuratively) that time is a dimension, and the map rotation as non-relativistic speeds is so tiny that you don't realize that t changes along with x, y, z. But it does. It would be bizarre if it didn't.
Here is one aspect of the conundrum: a certain photon travelling at the speed of light from the sun reaches the earth, which is relatively stationary vs the sun, in approx 8 minutes. It will obviously reach our rocket (which at the moment the photon was fired from the sun was at the same distance as the earth from the sun) some time later, depending on its relative speed to the sun. However, once the photon hits the spaceship it supposedly has the same speed as the speed of light hitting the earth.
I realize this axiom seems to have been experimentally proven, and that I probably just have not found the right key for me towards the understanding of it. Looking forward to that day, which might also lead me to understand how to fit the fact that the blueshift/redshift observed in light allows us to actually determine relative velocities. As well as understand how the expansion of space is a different kind of speed than normal speeds, allowing for the speeds greater than light that it does.
In the meantime I find some solace in the fact that I'm not the only one to find this bizarre - hence that whole linked article as I understand it. But thanks for your effort.