Leave the option open, except in emergencies, for the student to accept or refuse counseling. If the student is skeptical or reluctant for whatever reason, simply express your acceptance of those feelings so that your own relationship with the student is not jeopardized. Even if the student did not accept your attempted referral it will show your continued interest. Students often have a number of concerns about counseling and seeking assistance that, if not directly discussed, can deter them from acting upon a referral. It is useful to anticipate these issues and subsequently to make responses that are factual, encouraging, and appropriate.
People go to counseling for all kinds of problems.
The UCA Counseling Center sees 300 students a year for individual counseling. Going for counseling is a sign of weakness. It shows I can't handle my own problems. You are capable of handling most of your problems. There are some, however, that are difficult to handle alone.