Board Thread:The Reference Desk/@comment-29907559-20190907210239/@comment-6032121-20190907211228

The episode itself answers that fairly thoroughly, I think. The Doctor finds out that Susan has fallen in love with David Campbell, but also overhears her telling David that she cannot stay with him because she has to continue traveling with her grandfather so she can take care of him (the First Doctor is an old man of frail constitution and unreliable mental powers, do recall). So, knowing she won't let herself stay and be happy on her own, the Doctor removes the choice by leaving without her, leaving her to her guilt-free happiness.