It wasn't always so, though.
The idea that engagement rings = diamond rings is a modern one that grew out of a shrewd marketing ploy by the De Beers company. Despite the aura that surrounds them, diamonds are in truth neither rare nor special. They are expensive simply because the De Beers cartel has succeeded in controlling both supply and demand.
In the early 1900s, diamonds were a common choice for engagement rings, but were considered just one option amongst many, and people were choosing diamonds less and less often. When folks did go the diamond route, they bought small, inexpensive ones, preferring to spend their money on other things. Needing to get people to buy the heaps of diamonds they were sitting on, in 1938 De Beers launched a decades-long, multi-million dollar press and advertising campaign that sought to imbue the jewels with romantic meaning and social status.