Ok, I would just like to give you a warning before I get started. What you are about to read is going to be very long, diviating, and eccentric as I have some very strong feelings about Apollo and NASA's work. I will try to isolate my answer down to a couple sentences to make it understandable. Now then let's begin!
The main thing I hate about NASA is they have a real knack for rushing things. When people are rushed they skip important steps like doing proper safety checks. In the case of most of NASA's failings, they have been the result of very quick deadlines that rush their engineers to complete projects. (Like foam falling off EVERY SINGLE MISSION!!! GRRR!!! WHY CAN'T PEOPLE REALIZE THAT THIS IS AN ISSUE?!! ...Sorry. I digress... That only caused crew death with the Columbia... CURSE YOU PAUL--ok. I'm done with the Columbia now. Back to Apollo...)
Going back to deadlines, NASA compared to other governmental organizations is very poorly funded. The United States government expects NASA to be able to work some engineering magic and send people to space for just a few million dollars. Over time, the funding that NASA has received has decreased immensely which put much pressure on theweek to increase the amount of products they released, in a shorter time, AND cheaper!
Although the root cause of Apollo 13 mission failure would be bad management, the actual space craft had become damaged and resulted in mission abortion. The Apollo XIII was damaged when the oxygen tank 10024X-TA0009 -- their second oxygen tank -- blew up, damaging their primary oxygen tank and causing loss of much of the crew's precious resources two hundred thousand miles away from Earth.
All of this would have been preventable if more safety tests had been run, and damaged parts replaced. This tank that had ruptured, had originally been damaged, and repaired, but was unable to empty properly. Someone had the smart idea to shoot 65-volts of DC power for 8 hours which finally evaporated the liquid oxygen, but damaged the tank in the process, something which was not deemed important as a possible issue during flight.
Starving and dehydrated, the Apollo crew was able to make it safely home through improvising with what they had on hand.
To reiterate my answer to your question:
The Apollo XIII failed because it was damaged when the oxygen tank 10024X-TA0009 -- their second oxygen tank -- blew up, damaging their primary oxygen tank and causing loss of much of the crew's precious resources two hundred thousand miles away from Earth.
Sorry for the long explanation. Does it make sense at least? :)
