Why do all organisms have an even number or chromosomes?

All organisms, leaving out a select few have to have an even amount of chromosomes because they all sexually reproduce. Therefore when they go through MeiOSis and Mitosis they need a even number to reproduce. If there was an odd number in Mitosis then one chromosome instead of 46-23 or 24-12 being evenly split would have to end up being 23-11.5 with a half which isn't possible.