I'll try and explain why Jains do not eat garlic (along with other rooted vegetables like onions and potatoes):
When taking out the entire plant, you also take out any organisms like bugs and such from their ecosystem, killing them in the process. Jains try and limit the amount of violence they cause (Ahimsa), so in turn they try and avoid eating rooted vegetables.
On top of this, by removing the whole plant you prevent them from sprouting again, which is effectively "killing" in Jainism.
All of this being said though, modern agriculture techniques kind of make this reasoning insignificant. Mass farming practices mean that all plants are effectively killed along with any organisms in that area when harvesting.
And to top it all off, many Jains do not follow this practice, at least in the US. Many of my family eat all of these things, maybe trying to avoid them during Paryushan (holy week).
By growing a lot more of it (which prevents the birth of whatever would have grown in its place, but that's an invisible effect and technically not killing).
Also, grow mixtures of plants together that naturally crowd out weeds, inhibit the spread of pests, and replenish certain nutrients like nitrogen. IMHO this is grossly under-studied but could become more relevant with smarter robotics.
Also by growing hardier (but usually less productive) varieties, and growing multiple varieties of the same base vegetable rather than a single one, while I don't think that's the case for macro-scale parasites (insects) it's common for e.g. fungi to only attack some varieties of a specific vegetable.
How do you even establish an initial batch of the crop large enough to crowd out all weeds, without killing the existing weeds to start with?
Plants are hypercompetitive and constantly fighting for space and resources. The only reason modern agriculture works is we are so effective at killing weeds with machines and herbicide. Otherwise crop fields would quickly be taken over by whatever grows the fastest.
I don't know how they do their farming in practice, but I'm pretty confident that it involves more land use and lower yields.
They may also adapt their diet to whatever is the most edible among the weeds. This year a grape vine mysteriously sprouted in my garden and started taking over before I realized what it was and murdered it to save the zucchinis. A Jain would probably be happy enough with the grapes. I had even considered adopting it.
Jain vegetarianism (strictly interpreted) bans root vegetables (amongst many other things), in Gujarat restaurants (already vegetarian) have special symbols to mark "jain-safe" items in the same way western restaurants might mark vegetarian or kosher/halal items.
None of the other replies have mentioned Hare Krishnas (an offshoot of Hinduism). They are vegetarian: not only do they not eat meat but they also avoid eggs – though dairy products are seemingly alright. They distribute vegetarian food to the homeless and have a number of vegetarian restaurants around the world (mostly branded as Govinda's). As a vegetarian for 20 years or so, I tried their restaurants a number of times but the lack of onions or garlic put me off their food.
At the time, I asked them about this and the reply was that onions and garlic are considered to be stimulants and spiritually bad for you. The following article further elaborates on this explanation (best consumed with a pinch of salt): http://www.krishna.com/domains/d6.krishna.com/why-no-garlic-...
I've never heard of this. What religions ban garlic? (and pity for them, I love it!)