You can tell the candidate that you decided not to move forward with their application because they wouldn't be a fit for the position, they lacked relevant education or experience, or that the company decided to move in another direction. To act in a non-discriminatory manner, ensure that the reasons you won't be pursuing a certain candidate don't fall into one of the EEOC's protected areas.
The simplest and safest explanation for why you're not moving forward is that they were simply not a good match for the position. Being polite and nonspecific hopefully leaves open the possibility of the candidate reaching out to the company again in the future, as other opportunities arise.
In the case of a candidate you like but who simply doesn't fit at this time, you have a great opportunity to offer on-point constructive feedback and coaching. After all, this may be a candidate you want to hear from again in the future.
However you choose to communicate rejection, keep it respectful. Every interaction you have with a candidate has the potential to either leave a bad taste or create a positive impression. You can use this opportunity to benefit your organization.
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