I can promise you that you need to eat more. We can help tell you a figure of that if you can post your height, weight, age, and daily activity level.
As for your other question of why you need to eat to lose weight here is a very simple run down of how it works.
3500 calories make up 1 pound of fat. Now lets say in one day your body to maintain itself at your current weight needs 2000 calories. You may be thinking great I will just take in 1000 calories and i will be at my goal in no time! Doesnt work like that. If you take in to few calories your body will freak out so to speak and go into starvation mode. Meaning that all that yummy fat you are trying to get rid of gets held on to tighty because its afraid its not going to get enough food and therefore doesnt want to lose what it has.
Not only that it will eat into your muscle and basically make it to where when you do give in a eat (cause you will) that all that stuff is going to be instantly stored. This is why people lose weight (not nessesarly fat) fast, then eat a few big meals and bam are right back where they started or even worse.
The best thing to do is figure out how many calories you need to maintain and then subtract 400-500 calories. Your meal plan is just horrible. You need 1 protein and carb for every meal. Do starchy/simple carbs in the morning/pre workout (100% whole wheat grains, oatmeal, potatoes,fruits) and fiberous carbs (veggies) in the evening. Eat 5-6 times a day. So if you can have 1500 calories then you should have 300 calories very meal. You don't even seem to be getting that in two of your meals!
Combine the right diet with cardio 5 times a week and strength training (you wont get big) 2-3 days a week and then you will see real results. Please start eating some food!