The Russian frost does wonders for my health;
Anew I fall in love with life's routine:
Betimes I'm soothed by dreams, betimes by hunger caught;
The blood flows free and easy in my heart,
Abrim with passion; once again, I'm happy, young,
I'm full of life - such is my organism
(Excuse me for this awful prosaism)
Здоровью моему полезен русской холод;
К привычкам бытия вновь чувствую любовь:
Чредой слетает сон, чредой находит голод;
Легко и радостно играет в сердце кровь,
Желания кипят — я снова счастлив, молод,
Я снова жизни полн — таков мой организм
(Извольте мне простить ненужный прозаизм).
Whom better to quote in the fall than Pushkin? :)
(from the poem "Autumn")

Check Your Motives
...However, the article seems to be referring to people who annoy you personally. And in that case, you would have to be very careful to point out mistakes in a way that is not merely serving your own needs, but is constructive to the other person. There is a fine line between what is simply a personality difference and what is inappropriate behavior.
How do you know that you aren't the crazy one? Think carefully about that before confronting someone.
If someone is letting me know that I'm being offensive, the way that message is delivered to me is very important. Being confronted with a list of "grievances" is not something that I would respond well to. I wouldn't want to feel like I was being plotted against. It's important to think before you speak, but waiting a week while you form a good argument borders on manipulation.
You Don't Have to be Best Friends
I agree that there are some people with whom we're incompatible for one reason or another, and in some cases we can avoid close contact with them. This can save unnecessary stress and senseless arguments. Or we can avoid certain conversation topics.
However, is it really necessary to go through the whole process of telling a person what's wrong with him, if you plan to cut ties? Wouldn't it be better to just walk away peacefully?
Love Them or Leave Them
Also, I find that a lot of the time, these "crazy people" are the ones I'm closest to...my friends, family, co-workers, and fellow church members! And I wouldn't have noticed their "annoying" behavior if I hadn't spent a lot of time with them. If I'm going to hand out warnings or "break up" with each person who annoys me, I'm not going to get very far in my personal relationships. I'm not going to die to myself, and won't do much growing.
You can apply this to a simple case of sibling rivalry. What do you do with kids who keep getting on each other's nerves? One or both of them might need a time-out to calm down! But in a case where feelings have been hurt or injury inflicted, confrontation is needed. Repetitive conflict will need a stronger dose of intervention. But you can't separate the siblings indefinitely; they are a part of each other's lives. Rather than designating one of them the naughty one who is socially unfit, they need to learn to compromise.
I guess the article is just another example of how the Gospel is missing from the way people live their everyday lives. Everything is about "me" and getting rid of those things that stand in the way of my own success.
Is it any wonder divorce is so rampant? If you've been through a complicated situation, I am not trying to minimize your pain. I just think that we too often hear the message that we can control everything, or shut something out that God wants to use to make us stronger.
What I Would Have Written
My modified advice would be:
-if it's a person you don't want or have to see regularly, just keep your mouth shut and find ways to ignore the behavior. Let go of your preferences temporarily.
-if it's a person you plan to spend a lot of time with, find ways to either get used to the issue that's bothering you, or confront the person as quickly and humbly as possible, so you can move ahead.
-always check your motives!