I could never get my head around it in 4E and it was one of the reasons we gave up playing that edition. I put it in the same category as Evasion for Rogues in 3E as I've grown to dislike that too, but then I've been playing for 30 years.
Can you explain why this is difficult for you to understand? Honest question, because to me I can't see that bit. I can only see how it's mechanically boring.
I mean, presumably you can understand this situation:
1) Spells which do half-damage when saved against or when they miss (in 4E, a spell "missing" is the same exact thing as someone saving against it in another edition).
This isn't just AE spells, either - lots of spells in various editions of D&D do half-damage even if you "save", even if they were something you could, realistically, have dodged all of.
So why is the following situation hard for you to process:
2) An ability which isn't a spell, but might well still be "magic", which does half-damage on a save/miss.
I could understand not understand or disliking all three - say, you never liked that Fireball, other spells, and dragon breath weapons and so on were save-for-half in 1E and 2E, and didn't like it that this continued in 3E and 4E. That's where I'm at, by and large (understand-but-dislike, in my case). I think zero-damage-on-miss is more interesting in all cases. What I can't understand is why someone is fine with Fireball, breath weapons, some other physical effects and the like being save-for-half (which is precisely and exactly the same thing as half-on-miss), but not understand or like other, similar effects doing half-on-save/miss. That's confusing to me.
I kind of wonder if a lot of it isn't veiled "Fighters can't have nice things", but when we're talking 4E, we're talking an awful lot of magic-users operating this way too.