Because

Your child was born on June 20th.
Last year (2015), Father's Day was June 21st, so you celebrated it the day after your child was born.
Since 2016 is a leap year, Father's Day was on the 19th, not the 20th, so you celebrated Father's Day the second time before your child turned 1.

Alternatively,

Father's Day is the third Sunday in June, so on some years it jumps back 6 days instead of 1 (when June 1st becomes a Sunday again).
This would also allow for a scenario similar to the previous one to happen, but didn't specifically happen recently as described in the question.

Because

Your child was born on June 20th.
Last year (2015), Father's Day was June 21st, so you celebrated it the day after your child was born.
Since 2016 is a leap year, Father's Day was on the 19th, not the 20th, so you celebrated Father's Day the second time before your child turned 1.