1: Everything comes down to numbers in the end. Yes, that too. Yes, even that. —Arithmancy is not so much an actual field of study as it is this idea, seen through a thousand different minds.
2: Numbers do not lie. They may be wrong, they may try to trick you, they may force you to sit alone at a desk for days as you go through them digit by digit in vain hopes of finding some infinitesimal error, drowning in your own despair . . . but unlike everything else in life, they do not lie. Cold comfort is better than none.
3: It makes sense. Your parents look at you with a sense of vague bemusement when you go on with such excitement about learning to make pineapples tapdance, but they light right up as soon as you begin to talk about statistics and graphs. Even if the wizarding world goes down in flames tomorrow, a head for figures can get you into any university in the world.
4: All spells can be written numerically. The most accepted theory goes that the bad Latin and the wand movements are simply direct shorthand for complex strings of numbers, however, this has been proven to be inaccurate. It is possible to entirely re-write a spell with arithmancy, cast it with the normal words and motions, and have the revised effect occur. This requires further research, but no one has time at the moment.
5: It makes many wizards uncomfortable. In Britain's magical community, the links between cause and effect, action and consequences, are often very tenuous, due to the nature of the European style of magic. Wave a wand, say some words, and bang! Bob's your uncle. Since arithmancy depends entirely on one's ability quantify objects and follow exact chains of logic, it requires a different mindset.
6: This being the case, it should surprise very few to learn that arithmancy is often a favorite field of those from the non-magical world. In fact, it is one of the few where such people notably outshine those who grew up surrounded by magic.
7: Arithmancers tend to be very grounded in reality. Hard numbers (or even soft ones) have a steadying effect on one's perception. This can be uncomfortable, as you well know—anyone who's spent much time considering reality knows that—but it's very useful, especially among people who customarily enchant their hats to blink yellow polka dots on important holidays.
8: Witches who take a significant amount of 'hard' extracurriculars—Arithmancy, Runes, Alchemy, et cetera—are .3 times more likely to get a job than those who don't. Muggleborn students who focus intensively on their schoolwork are 70% as likely to succeed in their careers as Pureblood students who do not. Statistically speaking, girls who are familiar with numbers are five times less likely to die by another's wand. All this being the case—well, you do the math.
9: Although it is a relatively recent branch of study in Britain, arithmancy is and has since its inception been one of the fastest-growing fields in the entire world. As an Arithmancer, you'll never lack for work—there will always be another spell to develop, another building to plan, another idea to make viable.
10: Safety in numbers. Everyone knows that.