Hmm.. The inside is like a fruit, but the outside is like a nut.
I think it's a fruit, it has juice, and nuts can't have juice. Some fruits have hard coatings, but a coconut's coating is like a thicker, harder outside than most fruits. Maybe it's only called a coconut because the people that created that name didn't think about the inside, just the hard outside. Why don't we find some definitions.
Fruit
1. (botany) The seed-bearing part of a plant, often edible, colorful and fragrant, produced from a floral ovary after fertilization.
2. (nutrition) Any sweet, edible part of a plant that resembles fruit, even if it does not develop from a floral ovary; also used in a technically imprecise sense for some sweet or sweetish vegetables, such as rhubarb, that resemble a true fruit or are used in cookery as if they were
a fruit.
Nut
A hard-shelled seed.
Coconut
The fruit of the coco palm, Cocos nucifera, having a fibrous husk surrounding a large seed.
Now lets see. What makes it a fruit?
-The fruit of the coco palm..
-The coconut is "a sweet, edible part of a plant.."
-It's the "seed-bearing part of a plant.. "
What makes it a nut? Nothing. The "hard-shelled seed" is inside the flesh.
So, yep, it's a fruit. All definitions from Wiktionary.