I've been mulling over this today.
There's a traditional horticulture approach that includes soil science, basic botany and entomology, fertilizers and composting, learning about ornamental, herbaceous, and woody plants, integrated pest management and pesticide safety.
In the U.S., many of our Master Gardener programs coordinated by land grant universities follow a curriculum based on this approach. Some states have diverged into sustainable gardening (Oregon, Illinois, Maine, and others) or EarthKind gardening at Texas A&M.
But as a passionate gardener, who was 'trained' as a plant ecologist, I'm not sure that this is exactly what you need to know to be a good gardener.
Do you really need to know about soil chemistry and cations, and how that works?
Of course, understanding your soil's characteristics, building soil food webs, increasing soil health, and adding organic matter is important to any garden. If you want to grow plants that require nutrient-rich soil (think vegetables, which are seasonally harvested), soil enrichment is incredibly important, whether it's from organic cover crops or fossil-fuel dependent 10-10-10. But adding mulch and compost, along with organic fertilizers, takes care of these needs without learning about cation balance.
So what about Basic Botany and Entomology?
Understanding how plants grow, reproduce, how they're related, how they spread -- these are all important topics within 'Basic Botany.' Ditto for 'Entomology' and insects of all sorts.
I DO wish I had taken an enlightened Entomology class somewhere along the way in my 'formal' training. But there's an awful lot of dull stuff that masquerades as Basic Botany out there; trust me, I've had to teach it. And Entomology is equally dreadful, if mishandled.
And not to mention plant pathology (all the things that can go wrong) and often do, if your garden isn't in balance or has had pests introduced (root-knot nematodes, in my case).
Uh, pesticide safety? Excellent idea, but I think I'll just say no. I'm frankly relying on pest control from my wildlife-friendly garden.
What do you think you need to know to be a good gardener? To grow vegetables, flowers, shrubs, trees, etc.?
Let me know.