In many of the math classes you have taken so far, you likely were asked to provide work to justify your answer. This allowed your teachers to get an idea of your reasoning in case you made a mistake that lead to an incorrect answer. If you forgot a negative sign or multiplied 2 by 3 to get 9, your teacher could approximately reconstruct your problem solving process and perhaps award partial credit. Good organization and presentation was helpful, of course (and probably led to more partial credit), but it may not have been emphasized. Quite often the most important thing was the correct answer, and the work leading to the answer was secondary in importance.
The purpose of a proof is to convince the reader that a claim is true. The wording must be precise and logical, and organization and presentation is essential to a good proof. Any error in logic anywhere in the proof process invalidates the proof.
Wording is important; for example, if you wish to use an even number, do NOT say
x = EVEN
The equals sign in mathematics has a definite meaning. Evenness is a property of an infinite subset of integers and cannot be "equal" to a particular integer. Rather say
Let x be an integer such that x = 2m, where m is an integer.
Here we establish x as
By definition, any even integer must be an integer multiple of 2.
Within a proof you should use precise English sentences that correctly and clearly connect your main points. You need not be too wordy, but your goal is to provide enough information so that a mathematically-trained reader never comes to a place within the proof and says "what?" or "how come?"
So, a proof is not some hurried work you provide to "get an answer." With a proof you KNOW the answer and the work justifying it is the valuable part. Unlike most of your work in other math courses, when focusing on a proof, the work is of primary importance, and the final answer is, in some sense, secondary in importance.