As the other responder pointed out, this is not a simple issue (also at some point we switched from Slovenia to Czechia). There are at least two ways the east/central/west distinction applies. The first is geographical - every point that claims to be the middle of Europe is in or to the east of Czechia (https://en.wikipedia.org/wiki/Geographical_midpoint_of_Europe), so geographically it's pretty clearly not eastern (which again, the original Wikipedia link also says - pretty sure they're not all Nazis).

Politically it's a more complex thing. A common American interpretation is "part of the Soviet bloc". By that definition, yes, eastern Europe. But, there's also a not uncommon perception that this means it's a not well off country that is behind because of communism (see the movie Eurotrip for an example in pop culture). People who are in those countries would like to not have this association, so "central" is a way to avoid the Cold War era east/west split.