Cannot present paper at conference. Instructor wants to move me to second author
Who presents a work should not affect its authorship.

Authorship is determined by the contribution to the publication.  That work is complete at the time when the publication is accepted and the camera-ready is submitted.  Now, it is entirely reasonable (and in fact common) for a paper to be presented by somebody other than the first author, and it's quite normal for the presenter to highlight their name in the presentation.  In no way, however, should that change the authorship of the paper.