Bad reasons for a date shift
A parallel interview is honestly not a good reason. The suggestion of having an appointment with another employer may make candidates look more coveted at first glance. The second, however, is an affront to the cancellation: you are only a second choice. And I'm not so motivated to work for you, because the other job is obviously more important to me. This makes the applicant immediately less credible and unattractive. Sure, there are candidates who can afford such a poker game. But the majority is not.
Cancellations with reference to a regular therapy are dangerous. For example, anyone who wishes to postpone the job interview because he or she always meets with the psychiatrist on the day or is being treated for chronic back pain nourishes doubts about his or her performance and mental health. In addition, no employee is required to provide such information. In that case, you should mention other reasons.
Scheduled doctor's appointment
Also, medical appointments are a double-edged sword: Who gets sick or has acute pain, does not need to postpone the doctor's appointment. However, these are not planned reasons, but at most surprisingly short-term (see above). On the other hand, a planned visit to the dentist or a regular preventive appointment can generally be postponed without endangering life and limb. In that case, the request for a date shift subtly sends a false signal to the prospective employer: the job does not seem to matter so much to you. This actually reduces chances - or could be critically questioned in the job interview.
The worst reason of all, however, is to have no reason whatsoever. "I'm sorry, I cannot” or "I am prevented at the appointment" are no reasons. Equally incomprehensible is the sole wish that one would rather have another appointment. Job interviews are not a request concert after all. A lapidary and not very plausible rejection, therefore always expresses low esteem - especially since the employer has already expressed interest in the invitation. It's like asking his love (s): "Will you marry me?" The one who says "Yes" - and one replies: "Great, but not on Thursday, since I meet with friends ... "