Short answer: **You should'nt**.

**Reason 1: nutritional needs.**

Dogs, just like humans, need a varied diet including the right amount of protein, fiber, fat, minerals, vitamins and other nutritions.

Dogs evolved from wolves, who get their nutrition almost exclusively from animals they hunt. They evolved to exract nutrients from muscle meat, intestines, skin, cartilages and even bone, but not from roots, fruits or vegetables.

We humans evolved from omnivores, so we can extract nutrients from animal and plant sources, which gives us the opportunity to switch to a purely vegetarian diet. But even then we have to take care to eat a healthy, varied diet that includes all the nutrients we need.

If you want to feed your dog a purely vegetarian diet, you needto do **a lot of research** to make it healthy for her or buy commercial food where you need to trust that the manufacturer did this research for you and formulated the food accordingly.

For more information, please refer to [How can I ensure that homemade dog food is healthy for my dog?][1].

**Reason 2: poisonous vegetables**

Some common ingredients in human food are actually poisons. We can eat them anyways because either our digestive system evolved to neutralize them or our big bodies can tolerate a higher amount of them. The same amount could be poisonous for a dog. Some of those common ingredients include:

 - Any alcohol
 - Chocolate
 - Onion
 - Garlick
 - Milk and milk products

Please read more in [Are onions dangerous for my cat or dog and why?][2] and do a google search. There are more vegetables that cause dogs discomfort due to bloating or other digestive issues.

**Reason 3: the signs of your/her body**

I'm sure you've heard about pregnant women suddenly craving pickles and ice cream, sometimes at the same time. This is her body sending signs that she needs certain nutrients more than usual now. The same happens to your dog, too, but in reverse. Her body tells her that she doesn't need whatever is in your home made food, but something else that she doesn't get from you.

**Reason 4: your own reasons for a vegetarian diet**

If you are a vegetarian yourself, what is the reason? Most people either want to save the environment or want to avoid animal suffering. But that must include your own pet, for which you took responsibility. You cannot voluntarily or unknowingly cause your own dog suffering to "save" other animals. 

You already see that your dog rather suffers hunger than eating the vegetarian food. 


  [1]: https://pets.stackexchange.com/q/501/12501
  [2]: https://pets.stackexchange.com/q/796/12501