Why do some species go extinct without significant evolutionary changes?

Q: Why do some species go extinct without significant evolutionary changes, even though they're part of the evolutionary process?
Krishna:

It is widely thought that the extinction of elephant birds was a result of human activity

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Evolution needs these conditions to succeed:

Some species go extinct without significant evolutionary changes because they lack the necessary genetic diversity to adapt to environmental changes. This can be due to several factors:

Limited Genetic Variation: A species with limited genetic variation is more vulnerable to extinction. It is akin to a building constructed with brittle materials, which is more likely to collapse under stress.
There must be differences, however slight, between different individuals in a population.
Those differences must be heritable, and those differences must lead to differences, however slight, in reproductive success. If you have those characteristics, you have evolution. 
Habitat Loss: Fragmentation and destruction of natural habitats reduce the area available for species to live and reproduce, isolating populations and reducing genetic diversity.
Inability to Disperse: Species that require large territories or are unable to disperse easily between patches are at risk of local extinction.

Lack of Adaptation: Some species may not evolve the necessary adaptations to survive in new environments, leading to extinction.

These factors contribute to the extinction of species that are part of the evolutionary process but do not have the genetic or environmental advantages that allow them to persist.

The causes for large-scale extinction in recent times are multifaceted and include human activities, natural disasters, and environmental changes. Here are some of the key causes identified:
Human Activities: The most significant factor contributing to mass extinction is human intervention. This includes habitat destruction, over-exploitation of resources, pollution, and introduction of invasive species.

Natural Disasters: Natural disasters such as volcanic eruptions, earthquakes, and meteorite impacts have also played a role in mass extinction events.

Environmental Changes: Changes in climate, ocean chemistry, and land use patterns have affected species' habitats and survival.

These factors have led to a significant decline in biodiversity, with many species facing extinction. It is crucial to address these issues to prevent further loss of biodiversity and protect the planet's ecosystems.
You must give enough time for the species to evolve. If environmental changes are very rapid, like human beings are causing right now, the organisms which can't cope with the changes will go extinct.