Apparently, if Germany bails out the PIGS (Portugal, Italy, Greece, Spain), it will cost Germany about 1,000 euros per capita. Germans naturally balk at having to send a thousand euros down to the lazy bums (incidentally, the national stereotypes are wrong: Italians work longer hours than Germans, but it's similar to how a poor Vietnamese farmer works longer hours than an American farmer -- the American has more machines and more land and is therefore more productive).
On the other hand, if these countries default and have to leave the euro for their second-tier currencies, then German banks will lose enough that every German will in effect lose 7,000 euros per head the first year and incur smaller losses in future years. That's because the loans that the banks have on their books are worth far less.
So, is it rational to just bail the countries out? I'm not sure. Because you can be sure that it's not going to stop with this one-time. There will be another bailout a few years now, and as these things go, that bailout is going to be more expensive than this one. Therefore, it's probably time to stop throwing good money after bad. I don't think Germany's reluctance to carry out a bailout is irrational.