Why do people eat back exercise calories?

You want to prevent your body from going into starvation mode, so your input minus output calories should total a certain minimum number of calories (for me it's 1200). If you consume less than that, your metabolism might slow down, defeating the purpose. Any other type of calorie total should be supervised by a doctor.

because thats the way MFP was designed.

Here is how it works, in a simplified manner:

You tell MFP: I want to lose 1lb per week.

MFP says: Okay, you need to eat X calories per day in order to lose 1lb/week, without exercise.

You do what MFP says, but then you decide to exercise and you burn an additional 400 calories. MFP then says "Hey, I told you to eat X per day to lose 1lb/week without exercise. You exercised, now you're going to lose it too fast and that's not ideal. Now I want you to eat X+400".

the point of exercise is to get fit. eating less is for losing weight but you still have to properly fuel your body

Also remember that you are already set up to have a lower caloric intake to aid in your weight loss. If you are set up for 1200 calories then burn 500, your body would only have consumed 700 calories to sustain itself. Not nearly enough!!
Exercise will burn your fat and keep your metabolism moving and keep you healthy. It's about balance, not extremem deficite.
Good luck!

Whatever would we do without someone starting a new thread on this every five minutes?

I don't even like calling it "eating back" the calories. They're not bonus. They're earned. The calorie deficit is already there whether or not you exercise. If you burn a lot of calories and don't replace then, the calorie deficit becomes too large.

MFP calculates your calories differently than other plans, which makes it confusing for those just starting out. Most calorie counting plans will ask for your age, weight, height, how active you are, and how much exercise you're going to do, and figures out how many calories you should eat from that.

MFP is more precise. It takes your age, weight, height, and activity level, then deducts the number of calories you'd need to lose (or gain) weight from that. The amount you SAY you're going to exercise doesn't play into it, so you'll lose if you exercise or not. The calories you burn through exercise isn't tallied into your total UNLESS and UNTIL you do the exercise.

Example: Another site might suggest you eat 1500 calories a day, estimating 30 minutes of moderate cardio exercise. MFP will say to eat 1200 calories, then if you do that 30 minutes of cardio, you'll "earn" another 300, giving you... the same 1500 calories the other site suggested.

If you don't eat those earned calories, you could create too large of a calorie deficit. It's not just a simple matter of calories in vs calories out... if your body doesn't have the right nutrients, it's much harder to lose weight. Food is fuel and if you exercise like a madman, you need more fuel.

If you don't want to bother with the whole exercise calorie thing, you should adjust your activity level to include your normal daily activity AND the amount you exercise.