Vegetarianism as a diet excludes the consumption of animal flesh, since eggs technically are vegetarian, they do not contain any animal flesh. People who include eggs in their diet, while abstaining from eating chicken, pigs, fish and all the other animals can be called ovo-vegetarian – a vegetarian who eats eggs. With that logic, we can consider eggs safe for vegetarians, but they cannot be considered vegan for sure.
But most Indians believe that eggs are non-vegetarian and thus do not consume them if they practice vegetarianism.
Source: Thanks https://timesofindia.indiatimes.com/life-style/health-fitness/diet/are-eggs-vegetarian-or-non-vegetarian-the-answer-might-surprise-you/photostory/74284216.cms