Esp8266 - SoftwareSerial vs Serial problem

I'm using Arduino Nano and ESP8266.

When I setup like the picture and connect Arduino Nano to PC by USB: enter image description here

The ESP8266 properly works. (Arduino Nano is just used as a bridge)

I print and read from serial with a C# program, it correctly works.

What I send from C# program:

AT+CWJAP="APN", "Pass"

The message from ESP:

AT+CWJAP="APN", "Pass"
OK

But, when I change the setup as follows:

Green wire (green wire on picture) to Arduino Digital2 pin
Red wire (red wire on picture) to Arduino Digtal3 pin
Create a software serial from code (esp8266 = SoftwareSerial(2, 3))
What I send from SoftwareSerial:

AT+CWJAP="APN", "Pass"

The message from ESP:

AT+CWJAP="APN", "Pass"
ERROR

Do you have any ideas? Why isn't the result on SoftwareSerial identical to Serial?