You’re correct that your OS will pick a program and ask it to open the image. The OS will not ask the program to execute the image — that would be nonsense.
However, images are complex formats and often contain meta data (like the date and time when the picture was taken) and other parts that are not directly shown — you can hide stuff in there without affecting the image on the screen. So there might be hostile data lurking inside the image file.
Furthermore, program can have bugs, in particular buffer overflows. Briefly, a virus can exploit this by putting too large data into the meta data sections — larger than the program that decodes the image expects. The internal buffers overflow and with enough skill, a virus writer is able to put executable code into the right place in memory so that the program that decodes the image will end up executing the code. That way an innocent and “dead” file like an image can host an exploit.