Does the president have to explain why he vetoes a bill?

"veto" is not a legal term and the Word does not appear in the Constitution.

From the standpoint of logic, the President either vetoes a bill or he does not.

However, if he does not veto a bill, he can either sign it or ignore it and it becomes a law in either case , unless Congress adjourns before he has had 10 days to consider the bill. In this latter case, known as the 'pocket veto', the bill is vetoed if he does not sign it.