Here is why the current in all parts of a series circuit has to be the same. Think of the series circuit as a garden hose carrying water. The hose has a few kinks in it that restrict the flow of water. We push one gallon of water into one end of the hose and note that one gallon flows out the other end because there are no holes or leaks in the hose anywhere, and the hose itself does not create or destroy water.
Analogously, the electrical current that enters the series circuit must equal the current that leaves it, because there are no leaks in the circuit and the circuit itself does not create or destroy current.
What changes instead is that the pressure in the hose drops across each of the kinks in it, and the sum of those drops equals the original source pressure. In the circuit, the voltage drops across each resistor, and the sum of those drops equals the supply voltage.