Idealice is the past tense of the verb idealizar, meaning "to idealize". It's a fantastic word to describe the act of imagining someone as perfect or better than they really are, often ignoring their flaws.
In this emotional song, the singer laments, "Te idealice a mi lado en mis noches y días" (I idealized you by my side in my nights and days). She's not just apologizing to her ex; she's apologizing for creating a "false love story" by refusing to see the reality of the person she was with.
If you have ever apologized to someone when you were actually roasting them, this track by Mexican-American duo Ha*Ash will hit home immediately. The title says "Perdón, Perdón" (Forgive me, forgive me), but do not let the polite words fool you. It is dripping with sarcasm. Instead of begging for forgiveness, the singer mocks her own gullibility for trusting someone who clearly did not deserve it. She sings, Perdóname por ver colores en un cielo gris ("Forgive me for seeing colors in a gray sky") and blames herself for imagining he was sincere when he was looking at other people the whole time.
She takes every standard romantic cliché and turns it into self-directed blame, admitting Te idealicé ("I idealized you") and clung to the fantasy that he was the love of her life. Notice the phrase Que estúpida me vi ("How stupid I looked"), where me vi literally means "I saw myself," but in daily Spanish conversation, it means "I made a fool of myself" or "I looked so silly." By the time she hits the chorus, she drops all pretense of kindness to deliver the real punchline: Y te pido perdón por haber esperado demasiado de un perdedor ("And I ask your forgiveness for having expected too much from a loser"). It is blunt, petty, and deeply satisfying to sing along with.