To divide bitcoins an (almost) infinite number of times would require their representation as a floating point number.
If you don't know how that differs from an integer, then ask a maths teacher to point you to a book explaining real numbers.
Although computer chips from different manufacturers ought to get the same answer when subtracting one small floating point number from another, such as 0.0002 - 0.00000001, they sometimes don't quite match, due usually to different ways of rounding between a computer representation and a human readable decimal representation.  Try looking up the "Pentium Bug".

Setting a fixed 10^-8 minimum fraction allows such to be represented with integers for which all 64 bit arithmatic logic processors will get exactly the right answer.  For example 2000 satoshi - 1 satoshi = 1999 satoshi.  The purpose of bitcoin is to have worldwide money with which all the computers in the world can exactly agree that valid transactions are valid, and that fraudulent ones are not.  This can only be guaranteed by representation of bitcoin not with real numbers but with integer counting of satoshi.  It was presumably decided very early on not to count "bit cents" worth 0.01 bitcoins and use those as a minimum unit because it was not small enough for envisaged use cases such as kW-seconds electric car recharging bills.   Also real money with metal coins already struggles to make small enough metal pieces for half-penny coins, so there was no reason to copy what physical currency did.

Ask me about pegged coloured coin sidechains and sharding if you want more (possibly minority opinion) ideas for spending very tiny bitcoin quantities, possibly smaller than nanobitcoins, without clogging up the main international blockchain.