Your question is, I think, based upon a false presumption: that avian eggs are more fragile than those of other oviparous animals.
The paper Evolution of the Cleidoic Egg Among Reptilian Antecedents of Birds1 suggests that increased calcification of the avian eggshell is an evolutionary response to protect against predation and microorganisms, particularly in soil. The trade off was less permeability and water absorption. To offset that "cost," birds' eggs evolved the albumen or "egg white" which adds liquid content.
This is discussed more (and referenced) in Frank B. Gill's Ornithology2, which goes on to further explain that the shells additionally protect eggs from the weight of incubating parents.
Other functions, such as that of oxygen exchange, are permitted by the calcium shell due to microscopic pores. Also, crystalline calcite (the main ingredient of the shell) can be used by the embryo to form calcium in development of its bones.
1 Evolution of the Cleidoic Egg Among Reptilian Antecedents of Birds by Gary C Packard and Mary J Packard; American Zoologist, Volume 20, Issue 2, May 1980, Pages 351–362
2 Gill, Frank B.. Ornithology. United Kingdom: W. H. Freeman, 2007.