Diamonds are generally a 'good' engagement ring feature from the chemistry/physics stand-point:
Pearls will melt in a variety of acids like vinegar, along with many other 'organic' materials.
Some stones also have strange chemical interactions and can change color or will patina with age (Fluoric acid, water from hot-springs, etc).
Some stones are 'soft' and will scratch over time as they wear and may need to be replaced (Rhodo, peridot, etc)
Some stones can build up internal stresses as they age and will become brittle (highly unlikely though, though possible)
The index of refraction of many stones does not produce as large of a 'sparkle' that diamond does (though others like zircons will be much more 'sparklely')
Generally, diamonds are relatively inert chemically and very very hard to scratch or damage, all while having a good enough 'sparkle' and are able to be found in large quantities. Though their prices are currently absurd, they are a good choice from a materials standpoint.