ODT is an old format that was replaced by Office Open XML (OOXML). Microsoft switched to OOXML as the default format beginning with office 2007. Apple supports OOXML with TextEdit and has partial support for the current standard in Pages. OpenOffice offers
partial support for OOXML, with the latest LibreOffice fork of OpenOffice offering both read and write support for OOXML. No fork of OpenOffice has switched to the current OOXML standard as its default file format.
Microsoft supports ODT in Office for Windows. That was a result of the timing of the new standard. Years ago Microsoft had been under fire for not supporting open file formats. So Microsoft built in support for ODT expecting ODT to be adopted as the open
file standard. The standards body picked a better open format OOXML. The development cycle of Office 2008 for Mac was just beginning so Microsoft skipped ODT support in Office for Mac and went forward with the new standard - OOXML - as supporting a newly discontinued
standard seemed kinda dumb,
People resist change. There are billions of files in old prioprietary Office formats as well as ODT that people have yet to convert to OOXML. So far, these old formats are hanging on, much as RTF in its various incantations hangs around.
I stand by my advice to stick with the current standard, which is OOXML. Files saved in OOXML can be opened and used by every word processor I can think of. Compatibility problems are minimized.