How do discontinuities cause reflections?

If you have a long transmission line with characteristic impedance Z0 and somewhere along that line at point P it changes to Z1, you will have partial reflection and partial transmission at P.

But how and why does it happen? Is it because of inductance and back emf? If so does it purely RC transmission line that changes in impedance not reflect?

Is it possible for a discontinuity to not cause a reflection?

It's a law of physics..Electromagnetic Waves are reflected while they are changing the medium if the mediums are different.
You can imagine that as a mirror.If mirror is semi-transparent, some waves will continue some of them will be reflected.If the mirror is fully dense, all waves will be reflected..

Observing results of electric field distribution gave me another idea: even without knowing physics behind it we may use very simple FDTD formulas for E and H fields and see how a pulse propagates through line Z0 over time reaching discontinuity step to line Z1. So without deep knowledge we may first analyze how these simple formulas with few additions/divisions/multiplications allow numbers propagate through 3d array over time. It reminds me some multipass image convolution processing algorithm, except it uses different kernels for dielectric and conductor. With this prior experience it may be much easier to understand theory.

Look at this example of sea water waves reflecting off a wall.
https://www.youtube.com/watch?v=NEVtNJ_tcfg

Now imagine a signal traveling down a wide trace that suddenly narrows. That's like a partial wall and will partially reflect. In general that's what an impedance mismatch is.

you need to read a entry level paper on how a transmission line works.
It is easy to digest, but a little beyond the scope of a forum such as this to explain it all.

Basically, a transmission line allows signals to propagate in both directions, and the boundary conditions dictate exactly what the reflected signal will look like

So imagine you have a transmission line of impedance Zo1, followed by another line of Zo2. When you launch a wave into the Zo1 line, the voltage and current are related by impedance of the first part Zo1. But the moment the wave reaches the segment of T-Line with a different impedance, the voltage and current relationship are related by the impedance of the second segment. So the voltage and current at that point must change to satisfy the impedance relationship of the second line, and thus a wave is reflected back!