Why do people assume 28 oxygens in chlorite mineral formula?
It doesn't mean that there are 28 oxygen atoms.  It means a charge equivalent of 28 oxide anions, considering that each oxide anion has a -2 charge and each hydroxide anion has a -1 charge.  

This is based on the chlorite having an formula including $\ce{O20(OH)16}$

For example see $\ce{Mg10Al2(Si6Al2)O20(OH)16}$ in The effect of Cr on chlorite stability and the appearance of a new Al-rich silicate

In otherwords, as explained in OCTAHEDRAL OCCUPANCY AND THE CHEMICAL
COMPOSITION OF DIAGENETIC (LOW-TEMPERATURE) CHLORITES


  All chlorite analyses were re-calculated as chlorite structural formulae on the basis of 28 oxygen equivalents (56 negative charges) i.e. assuming an ideal anion framework of $\ce{O20(OH)16}$