Looking at "neelkamal" (blue lotus), Aisha thinks it is like "mata-pita" — two equal things joined…

Why

Aisha picked up a pattern from the previous example — two equal things joined by 'and' — but that pattern applies only to one kind of compound (dvandva), not every compound. In 'नीलकमल', 'नीला' isn't an equal partner at all; it describes a QUALITY of 'कमल' (its colour) — telling us what kind of lotus, i.e. 'नीला कमल' (a blue lotus). This kind of compound is called कर्मधारय समास (karmadharaya samas), where one part describes or identifies the other, rather than the two being equal partners. Test it: strip 'माता-पिता' apart — 'माता और पिता' names two separate, equal people; try the same with 'नीलकमल' — 'नीला और कमल' sounds odd, because 'नीला' isn't a separate thing, it's the lotus's colour. Her brother is right: 'नीलकमल' means 'नीला कमल' — here one word describes the other's quality; this is कर्मधारय समास (karmadharaya), not dvandva.