Longing for a relationship selflessly is intimacy because you are not trying to know somebody for a selfish gain.
You still don't get it. Intimacy isn't about selflessness or sacrifice. It is nothing more or less than knowledge and understanding. It nearly always seems to be used in conjunction with emotion - so there's that element of feeling as well - but it's the knowledge that's the key. Acting selflessly can be an expression of intimacy - although frankly it's a pretty vague intimacy - but it's far from the only valid expression.
Perhaps hate is a better word
Hate is an emotion bred of intimacy. It's that rage and sadness and fear that you feel when someone or something you loved has failed or fallen in your eyes. It cannot exist unless you were intimate with something, whether it's the target of your hate or something else. Hate is about betrayal, and it's as much of an attractive force as love is. You can't hate something from 10,000 miles away. You have to be right up close, where you can release it properly. That's why war can be intimate. When you see the face of the enemy every day, and you see the hurt and the pain it causes you, and you know that it's for no good reason at all, that's when you can be intimate with an enemy.