This means that he was both caregiver AND combatant to Liz during her formative years. The end result is the manufacture of a paranoid basket-case who wanted to make sure that people and situations were 'safe' before she allowed herself to deal with them. It also made her a jealous goof who only allowed certain people on the island in her head that kept her from the scary monsters and super-creeps that haunt her nightmares. Given that she believes that Daddy did his best to stop the Primeval Monster only to be stopped by Mommy because she wanted Daddy to herself or some such nonsense, I think it's safe to see why she and Elly never really saw eye to eye much and why she was the only girl allowed on that magic fantasy island of hers.
It seems rather obvious in hindsight that on some level she's not allowing herself to be aware of, she regards Elly (and, by extension, every other woman on the planet) as a threat to her 'innocent' desire to fling herself at whatever Daddy substitute she fixates on at any given time. Somewhere in that head that loves being in love with love is the belief that Elly is stopping John from doing his job of, if not outright killing her siblings and anyone else who gets in her way, than at least forcing him to grovel pathetically every day about what a bad and selfish person he and April and that evil career woman are for also wanting attention that should be all hers. This need to attack anyone who might make her feel uncomfortable tends to negate any tendency she might have for the feelings of empathy and remorse that are unknown to Pattersons and thus means that she'll be an anxious basket-case all of her life.