Tell the truth and sound crazy or make up an excuse

[Bijou]

It can become somebody's business is/when it impacts their life or relationships. OP feels some concern that her relationship has impacted her friendship and her absence has unintentionally hurt her friend's feeings.

I would agree if the person in question were a close relative (spouse, parent, child, sibling) of the OP, and it really did impact them on some personal level.  Otherwise, no.  I just don't think that you have to bare your soul to friends and acquaintances.