Let me belabor this point a bit further.
If two resistors are in series, then you can disconnect them from the circuit and replace them with a single resistor whose value is calculated by adding the values of the original two. After having done so, the total equivalent resistance of the entire circuit will remain the same. Look at the image in post # 91, and consider resistors 1 and 4. Imagine disconnecting them both, and trying to replace them with a single resistor. How would you connect that replacement? When you disconnect the two, you will have left #12 dangling in the breeze. If you tried to connect the replacement in series with #12, then you will have changed the total equivalent resistance of the entire circuit. Therefore, we conclude that 1 and 4 are not in series.
If two resistors are in parallel, then you can disconnect them from the circuit and replace them with a single resistor whose value is calculated using a slightly more complex formula. After having done so, the total equivalent resistance of the entire circuit will remain the same. Look at the image in post # 91, and consider resistors 1 and 2. Imagine disconnecting them both, and trying to replace them with a single resistor. How would you connect that replacement? Do you connect it to the 4/12 point, or to the 3/9 point? No matter how you try to connect the replacement, you will have changed the total equivalent resistance of the entire circuit. Therefore, we conclude that 1 and 2 are not in parallel.