I don't why. The alleged crime occurred in a foreign country, and the evidence presented to the host country was deemed sufficient for an arrest for an equivalent crime in the host nation. This is just the flip side of the old adage that the Internet erases International borders.

Would it really be better if the host county put the alleged criminal on trial for crime that wasn't committed in the host country at all? Some countries do that (specifically I'm thinking about Israel) I wonder what he ge practical difference is.

how Israel does that? are you refering to the nazi hunting?

No. Israel kidnaps Nazis from foreign countries to put them on trial in Israel. See Adolf Eichmann.

I was specifically thinking about Samuel Sheinbein who killed a classmate in Maryland then fled to Israel, claimed Israeli citizenship, and because he was now Israeli would not be extradited. Instead he was put on trial in Israel for murdering his classmate in the United States.[0]

What I did not know until now, is that because of the legal crisis this case caused, Israel changed their extradition law regarding people who were not residents of Israel at the time the crime was committed in an effort to avoid being seen as a safe haven for Jewish criminals.

[0] https://en.m.wikipedia.org/wiki/Samuel_Sheinbein

That doesn't make sense. Someone sending a bomb in the mail can't be extradited?

That's sort of a weird scenario, but I'd say no - sending the bomb in the mail should have been illegal in the country they sent it from, whether it's illegal or not in the destination country shouldn't matter.

And if it isn't?

I'd imagine that mail services of other countries would refuse to accept mail from a country where it's legal to send mailbombs. If they didn't, I'd expect them to be at least somewhat liable for the ensuing explosions.

Countries don't arrest/extradite people for actions that aren't criminal in said country.

Depends on whether the person is wanted in another country and whether the governments of the two have extradition treaties that would apply. Many do.

A dangerous line of thinking.... If someone were to take prescription meds that's legal in the country they bought and took them, why should they be extradited to a country that happen to not agree on the legality of those meds?

That is only analogous if that person were facilitating the transport of these medications to a country in which they were not legal.