Why is an egg narrow at one end and fat at the other?

why is an egg slim on one side and thick on the other?

You don't want to know. Seriously, it's pretty gross.

Well...this is just a guess. The person who said "It's pretty gross" was probably thinking what I am thinking. The narrow end ensures that the final ejection of the egg, from the bird into the nest, is a gentle trip. A perfectly round egg would tend to pop out.
Now, you may wonder why reptile eggs are round, huh? It is because reptile eggs are also rubbery, so there's no cracking hazard as with bird eggs.
That's my guess.