555 Timer astable mode, capacitor discharges only through R2, why?
To understand how C1 is discharged, you need to first understand how the 555 timer works. The 555 timer has a resistor divider with 2 taps and 3 equal value resistors which creates two reference voltages equal to 1/3 of VCC and 2/3 of VCC. If the voltage at the trigger input (pin 2) goes above 1/3 of VCC, the set input of the latch goes high and the output goes high. The reset of the latch happens only when you pull the reset pin (pin 4) low or when the voltage at the threshold pin (pin 6) goes higher than 2/3 of VCC (or the voltage at the control pin (pin 5) if you need to use a different reference).

There is another pin left, which is the discharge pin (pin 7). This is an open collector output and can be shorted to pin 1 (ground) if the output is low or high impedance if the output is high.

So, in your circuit, C1 starts charging through R1 and R2 when the output is high and the discharge pin is high impedance. As the voltage across C1 reaches 2/3 of VCC, the output goes low and the discharge pin is shorted to ground, discharging the capacitor through R2. There is a current through R1 equal to VCC/R1, but this current flows into the discharge pin, since it is shorted to ground.



Image source: Wikimedia - BlanchardJ / Public domain, from Wikipedia - 555 timer IC