Difficult to be exact since this is a 'speculation' but my thought line is as follows:
1. Matter is comprised of positively charged protons with negatively charged electrons whizzing around them.
2. Antimatter is comprised of negatively charged antiprotons with positively charged positrons whizzing around them.
3. The faster matter moves the slower it experiences time. Since antimatter is diametrically opposite to matter, could it experience the exact opposite, placing it in a different time space?
4. Due to this difference in time space matter and antimatter would seldom come in to contact with each other and could coexist.