Why get a chef's knife or santoku if I don't eat meat?

Even for meat eaters, almost all knife work is done on vegetables. Santukos and chef's knives are general purpose knives, with great utility on vegetables. Chinese cleavers are also general purpose knives, the functional equivalent in that culture to the chef's knife.

The advice offered to you in this question:

Which knife is best for somone just learning to cook?

does not change simply because you are a vegetarian.

I use boning and fillet knives most often when preparing meat, and a slicer knife when portioning it after cooking - heck, I use my kitchen shears more often than my chef's knife when prepping raw meats (especially poultry and fish).

The chef's knife is used to prepare veggies, which is where the bulk of any cuisine's prep is, vegetarian or not. It's designed to reduce aromatics like onions, carrots, peppers and celery into minced, diced or cubed pot-ready ingredients. You can get through almost any food prep task with a chef's knife, a paring knife and a bread knife.

If you like collecting and playing with fine knives in the kitchen (and that's as fine a hobby as any), there are some fruit and vegetable-specific knives you could benefit from trying out.

• Nakiri and Usubo - these are the knives used by japanese chefs expressly to prep vegetables. The nakiri is a more robust everyday knife, the usobo is meant for making exceptionally thin cuts. They are meant to chop rather than slice.
• Tomato knife - This is a serrated knife used to cut soft and fragile food, such as tomatoes or ripe peaches. It's thinner and more weildy than a bread knife, and a good accompaniment to thicker European chef's knife styles.
• Bird's Beak - This is used to tournee root vegetables, pare round fruit, and to make delicate and tricky garnish cuts.

Chinese chef's knife is a multipurpose tool, and (depending on weight and blade thickness) is very handy to slice, chop and dice vegetables.

The technique is to let the knife's weight to the work, i.e. cook exerts no or almost no force on the downstroke.

Moreover it also used to transfer sliced and chopped ingredients to a wok pan.

Have a look at videos where chefs use same or similar knife for almost anything.

Most santoku, and certainly nakiri/usuba, knives are not good at supporting cutting styles that rely on the tip rolling smoothly on the cutting board; santoku tips tend to offer a more limited angle before the tip catches into the cutting board instead of rolling - while this seems to support the knife very firmly, it can very abruptly stop doing so, ending in an imperfect cut or even an injury.

Also, the tip of a chef (or kiritsuke) knife is well suited to doing some paring/cleaning work without having to change knives...

Blades that have a very straight edge (nakiri) have their use for thin or depth-controlled cuts (hasselback anything ;)...

It is likely that your local asian grocer will have inexpensive knives in most of the common asian shapes, these might not be Wusthof quality but they tend to be sharp and easily resharpened, and still of a far better quality than an equally priced supermarket knife - these are useful to experiment and find out what blades you like working with....

That said, most every knife shape/style is SOMETIMES useful even in a fully vegetarian or vegan kitchen - just not as often. It helps to think in terms of techniques rather than ingredients that these were intended for. For example, one could consider the deba and yanagiba pure fish knives - or useful wherever you need to separate elastic from hard (eg various fruit prep tasks), or slice something with long smooth strokes (eg various bakery tasks).

My neighbor is a good cook and I do a lot of the prep work when I am over for a meal.

He really likes his santoku and encourages me to use it but I don't like it. I prefer a wide 6 inch cooks knife with as relatively flat blade for meat, vegetables, and fruit.

There are many tasks I like the point (better control):

• On slice down on an onion half to dice I don't slice the two ends all the way to the front.

• Slicing out the stem on a half strawberry.

• Clear out the interior on a pepper.

For pure fine mincing like parsley is the only time I prefer a santoku.