I don't know how old he is and what would prompt the family to be worried over his financial status when he can obviously take care of his basic needs. Maybe his family sees him as some lazy guy who earns money through illegal means. Him having a part time job while he invests would have been a very good distraction. All this would have been avoided if he didn't make mention of bitcoin in the first place. Anyway, if he must let them know how much he earns, then he should declare a false figure. There should always be a way out.
The purposes of declaration of a personal income and source of income relelates to privacy that matters for everyone.
Nobody has rights to ask you to disclose your personal information and income, source of income is part of your private information. Purposes of self declaration about your income and its source, depends on you, and very differently in cases if you intend doing this for inheritance of your family members, make impression that you are able to work and earn salary and can contribute to your family spendings; or it's other reasons.
If you don't want any family member to inherit your bitcoin, don't diclose private information about your work, investment and private keys.
If you don't want your family members to be angry with you, make sure you contribute part of your earnings to family spending weekly or monthly. It's fair and responsible contribution when you are a family member.
If you don't contribute to your family spending, they will have big questions and concern that you are lazy, don't work, and are irresponsible with the whole family.