On a relative level, because our habitual attitudes of self-cherishing cause endless grief for ourselves and others.
I too have a close relationship with pride and arrogance. You don't want to make things harder on yourself by thinking, "I
am arrogant, I
have such a problem with pride." Such statements strengthen the cause we need to work on: habitual fascination with and servitude to ideas of a self. Thankfully, it's all smoke and mirrors, so it's all workable.
I've noticed a tendency to feel disappointed when others don't give me recognition for X, Y, or Z. Especially in my workplace. "I did such a good job and no one even noticed. Huff!" What juicy stuff to work with! Instead of having to dig around to find the hindrances to our happiness, this one is so kind as to jump up and wave its arms for us.
There are lots of practices that help us be gentler towards ourselves. Our habit now may be a kind of protecting and hardening our views and tendencies when there's a little prickle in our sense of security. Maybe we only notice that prickle after someone points out we've been arrogant. But the reaction is the same: yikes, ouch. So what is really needed is an approach that catches when we're about to pull out our favorite security blanket of ego and let the prickle do its work
There are two practices I've found that are excellent for pride. The first is doing prostrations in front of the altar or a visualization of the Buddha, the Three Jewels, your guru, etc. Whether you do the five-point prostration where you kneel and touch the ground with your knees/legs, forehead, and two hands, or a full prostration where you lie face down outstretched, these help establish our awe and devotion to objects worthy of it. The latter full prostrations are considered more potent at disarming our pride. The suffering of arrogance and pride come from our ego wanting our full attention and service. Prostrations say there's something else worthy of that instead, and by offering our attention, devotion, aggregates, etc. to them, we don't offer them to the illusory ego. You can even offer your self-cherishing and arrogance when you prostrate. After all, you're not the first nor the last to have these problems (I'm right there with you!). It can be helpful to feel you're practicing overcoming arrogance and pride for all the suffering beings who don't know about practice or don't even see there's a problem. You've been there, too. Turn that poison into bodhicitta.
Another practice I've found is great for ego reduction is the lojong mind trainings. It's more like a palette or toolkit of 59 mini practices, but some are truly excellent for turning our perspective on its head so we can see, "oh crap, I almost ran headlong into pride again. Whew!" It goes through many antidotes to self-cherishing. You may find the practices on emptiness cut through the solidity of ego right away. You may find the four thoughts that turn the mind to dharma (the "four preliminaries") do the trick. If not, then it includes tonglen to dampen ego by reversing the usual logic of good for me, bad for you. And to top it all off, you have ones that directly tackle ego: Drive all blames into one (#12), Be grateful to everyone (#13), Don't act with a twist (#36), All activities should be done with one intention (#39), and last of all, Don't expect applause (#59). You'll find a full range of commentary on each of these at http://lojongmindtraining.com/sectionSu ... ectionID=0
You can chew on one slogan a day in order, or pick ones that seem most potent for your situation. One that I return to very often is "Be grateful to everyone." When your ego gets nettled and inflates, or when someone else pops it, that person is a bodhisattva showing you the very things that trap you. Thank goodness for the rude clerk, grumpy friend, spouse who drives us insane. I've had the experience of being about to blow up into a huge drama at someone, then in a little angelic voice I heard Chekhawa say in my ear "No, no. Be grateful to everyone!" I wanted to throttle him. Then I realized I wanted to throttle a monk from the 12th century. It was my mind coming to save me from myself. I had to laugh
Also traditionally, I believe the common prescription for reducing self-cherishing is contemplating emptiness. You won't find a self to worship after all. It's like the man yelling at the boat that's about to crash into him on the river. He gets angrier and angrier, waving his arms, and the boat just picks up steam in the current and nearly capsizes him anyway. As he's about to give the person a good tongue lashing, he sees... the boat is empty. Ever had the feeling of the rug being pulled out from under you like that? No ego to be a problem, no problem to be a problem. That's an example of the practice of emptiness. It can be tricky though if you don't already have a foothold already, that ability to see the gap before you puff yourself right up.
Anyway, I hope this was helpful. Try not to be too hard on yourself. Speaking from experience, this is one of the most difficult fetters to overcome because it stems directly from the root of one of our most basic misconceptions: I'm here, I need X, give me Y or I can't Z. Do your best
If you feel that odd uncomfortable tingling of ego protesting at something, good humor will help. "Hi there, pride. What are you so worked up about? May all beings who feel this tickle be able to smile at it in this way and not get too upset about things."