J. L. Bell’s A Primer of Infinitesimal Analysis (an intro to synthetic differential geometry) begins with a series of quotes to motivate why we should think of the reals as containing infinitesimals. The quotes all involve the idea that philosophically speaking the continuum is an indivisible whole. This quote from Hermann Weyl is a typical example:
A true continuum is simply something connected in itself and cannot be split into separate pieces; that contradicts its true nature.
I find this line of reasoning completely unconvincing as motivation for allowing the reals to have nilpotent infinitesimals. I can grant, for the sake of argument, that maybe its unnatural that our model of the line can be split cleanly into two or more parts, but to me this is an argument for constructivism, not infinitesimals.