Why would a person who is very physically active need to take in more calorie than a person who is very inactive?

A Calorie is a measurement of "fuel" availability. If a person is VERY physically active, they need to take in more fuel to stay the same weight. Just like a car that drives more miles in a day needs more fuel than one that sits in a parking lot.

Depending on the size of the person, there's a base amount of calories needed to perform the requirements of the body, like fueling breathing and sitting and moving. The more you move, the more calories you use.

When you start using more calories per day than you take in, you start to lose weight. The fat gets converted to energy to fill in the extra calories needed to cover the amount taken in versus the amount needed to do all that moving. That's why you lose weight. Or, you take in more calories if you are very physically active and want to stay the same weight.