Why do we need resistors in led

LEDs have a fairly constant voltage across them, like 2.2V for a red LED, which only slightly rises with current. If you supply 3V to this LED without series resistor the LED will try to set for a voltage/current combination for this 3V. There's no current that goes with this kind of voltage, theoretically it would be 10s, maybe 100s of amperes, which would destroy the LED. And that's exactly what happens if your power supply can supply enough current.
So the solution is a series resistor. If your LED needs 20mA you can calculate for the red LED in the example

\$ R = \dfrac{\Delta V}{I} = \dfrac{3V - 2.2V}{20mA} = 40 \Omega\$

You may think that supplying 2.2V directly will also work, but that's not true. The slightest difference in LED or supply voltage may cause the LED to light very dim, very bright, or even destroy. A series resistor will ensure that slight differences in voltage have only a minor effect on the LED's current, provided that the voltage drop across the resistor is large enough.

The point is a LED is a diode anyway and diodes have very small internal resistance (in "forward" direction of course), so unless there's something else in series the overall resistance is very low and the current is barely limited and this barely limited current can damage the LED and overload the circuit that powers it.

So yes, you're totally right that the current is the same in each point of the circuit when elements are connected in series, but when you add a resistor you increase the overall resistance of the series and this decreases the current.

Always with the complicated answers ;-). Look at it this way. What happens when you put a wire across the terminals of a battery? In a perfect world you get infinite current which melts the wire. We call this a short curcuit. Because diodes are designed to have minimal forward resistance we get the same effect as a short. Put a resistor in there to provide something to resist against current to limit it down from infinity