Well if she is immortal she can't afford to make emotional attachment if she was to get along with seeing everyone else around her born and die over and over through the generations. It's the only way to cope with the immense emotional stress. And how could she possibly relate to them to begin with when they are so distant from each other? When one is so above the rest in terms of power and knowledge?
If she allowed herself to become that. If she allowed herself to become numb to the pain. Then she'd loss what makes her a pony. If she lost the power to feel attachment, that would be the first step to losing her empathy.
There was a fanfic (I didn't care to finish it and I don't remember the name nor do I care to learn what the name was) where Celestia HAD lost most of her attachment, and saw her ponies as a blur, a "multicolored blob that's only redeeming feature is that it didn't leave a slime trail in its wake" and went through everything in routine until she met Twilight and began to feel emotion again and though resealing Luna would be a trivial matter . . . until she realized she had lost the emotional attachment to make the Elements WORK and ended up sealed. Resulting in Twilight having to save her as in the episode.
Like I said, she could simply grow numb to the pain of watching loved ones come and go through the eons. Besides, the one pony she can truly relate to is Luna, and she's never going to die. Having an immortal sister who can understand the pain of losing loved ones can help take some of the weight off of her own shoulders.
Every time i see a picture like this, the little guys who live inside my body and keep it running have a conversation that goes like this:
"Attention workers, he's looking at pony pictures again!" "What's the cuteness level of the picture he's looking at?" "Sir, it's over 9000..." "Mother of God, he's not gonna handle it..." "Sir, he's starting to get a seizure!" "For Christ's sake, give him more insulin!" "Sir, he just passed out." "Goddamnit, that's the 4th time this week."