Quite some time I had classes on this - but I believe chemo (some at least?) is designed to attack cells with same growth-rate as cancer cells. So they're not attacking just everything in a non-discriminatory fashion - but cells with similar growth as cancer cells, become collateral damage, so to speak.

This is why some chemo will result in for example hairloss; Because the cancer you're being treated for, has the same growth rate as the cells in your hair - and thus the chemo will also kill those cells.