Headcanon: John Jameson likes Spider-Man not just because he
saved his life in ASM #1 but because Spider-Man’s sense of humour (especially
in the face of his father’s persecution of him) is something he respects and
resonates with him.
This is because as a man who’s lived through war, the loss
of his mother and growing up with Jonah appreciating a good joke (even when you
aren’t the person cracking it) was how John coped. That’s why he likes Spidey.