The phrase on the side is a tricky one, because it has several possible meanings.
If I had a cyst on my torso, and was going to have it removed next week, I could tell you that I was going to have surgery on the side.
Of course, in this context, we are referring to one of these two idiomatic meanings (definitions from NOAD):
on the side
1 in addition to one's regular job or as a subsidiary source of income : no one lived in the property, but the caretaker made a little on the side by renting rooms out.
2 secretly, esp. with regard to a relationship in addition to one's legal or regular partner : Brian had a mistress on the side.
There's nothing furtive going on here, so that rules out meaning #2. What the writer really means here:
Maybe I should take up surgery as part-time work.
In this context, the writer is trying to say that the two could learn a lot from each other: what comes natural to one is not nearly so simple for the other.
One more important detail: no one takes up surgery on the side. We might sell real estate on the side, we might tutor or teach on the side, or we might work in a restaurant or retail store on the side. But surgery is a skill and profession that requires years of intense training. So the writer here is being humorous. He doesn't really intend to take up surgery as an extra job, but he's reinforcing the notion that sometimes it's easy to forget how difficult something can be after we have been fully trained.