And that is a good question as well Martin. It just has seemed really odd, his actions. But then Ruby robbed us of ever knowing the answer.
Did it really? Would we have been able to trust implicitly whatever Oswald said? I think that whether Oswald lived or died people would still have to look at the facts to figure out what was most probable.
** Oswald arranged for a unique weeknight ride to where his wife was staying instead of the usual weekend ride.
** Oswald brought to work a long object wrapped in paper (it would be too embarrassing to be seen with curtain rods).
** Oswald was the only one at work who immediately left the Dealey Plaza area. Someone correct me if I am wrong but I understand a few others left the building to check out what happened from other people in the plaza. And then found themselves locked out of the building by the police. Only then did they go home.
** Oswald got on a bus and then immediately off when it was stuck in traffic.
** Oswald ordered his only taxi ride (quite an expense) that we know of during his life.
This seems pretty consistent to me. If Oswald lived and told me a different story, I probably would not believe him.