Setting "homework" for clients implies that no relevant work would otherwise occur between sessions. When clients fail to do their homework but achieve positive change anyway, the focus may fall on the former rather than the latter.
Physical therapies often entail a certain amount of work on the part of the client inbetween sessions with the therapist: daily exercises may be set, weekly diet sheets may be provided, medications may be prescribed.
Psychological therapies may also require work inbetween sessions. The notion that therapeutic change occurs only within sessions, in the presence of the therapist, is disproved by the evidence: the greatest portion of therapeutic change is attributable to factors entirely outwith therapy.
Some psychological therapies have followed the physical therapy model with the allocation of "homework". Some interventions do require directed effort outwith the therapeutic session (daily practice of relaxation exercises, keeping thought diaries, etc) There are problems both with labelling this as "homework" and with extending the practice beyond the acquisition of new skills and information.
Ask anyone which members of society are set "homework" and they will answer: schoolchildren. College students are more likely to be set "assignments", trainees may have "set reading" or "research", but "homework" is strongly associated with schoolchildren. The term denotes activity allocated to those who are (as yet) unable to direct their own learning.
When I have observed colleagues' sessions, I have been struck by the number of clients who have not performed their set homework. This revelation is usually made by the client in guilty tones, generally in response to a direct question rather than being volunteered. This often elicits a lecture from the therapist as to the importance of doing one's homework which certainly takes me, if not the client, straight back to school days. Is this where you want your clients?
When (if?) the discussion moves on from the client's "failure", it is usually revealed that some significant change in the client's life has occurred between sessions, just not the change anticipated in setting the homework. Setting homework implies that the client would not otherwise be working (constructively) on the problem, when the problems clients bring to therapy are usually those with which they are struggling on a daily basis.
If you feel inclined to set homework, consider waiting to see how your client makes use of the time between appointments without your direction. A constructive session should leave the client keen to apply the results. If you feel you must set an activity or goal, ask your client what they feel would be the best way to use the time until your next meeting.